4t ESO/4.04 EQUACIONS/4.04.2 Equació 2n grau/4.04.2.1 E2G1: ax^2+c=0 4.04.2.1.10 TEORIA: E2G1 ax^2+c=0

Equació incompleta I: ax²+c=0

Es resol com una equació de 1r grau:

traslladant els nombres a la dreta, sumant o restant
dividint pel coeficient de x².«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»50«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo»§#8660;«/mo»«mn»2«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»=«/mo»«mn»50«/mn»«mo»§#8660;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»=«/mo»«mn»25«/mn»«/math»

Després si és possible, es calculen les arrels positiva i negativa del membre de la dreta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»=«/mo»«mn»25«/mn»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»§#177;«/mo»«msqrt»«mn»25«/mn»«/msqrt»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»§#177;«/mo»«mn»5«/mn»«/math».

Si a·c < 0, té dues solucions oposades.

Si a·c > 0, no té solució.

]]> 0.0000000 0.0000000 0 4.04.2.1.10_1 TEORIA: E2G TIPUS1(GIF)

]]> 0.0000000 0.0000000 0 4.04.2.1.11Q E2G1: Resol ax^2+c=0 SolucionsRACIONALS Calculeu, si s'escau, les dues solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta:

si en té, escriu x=solució/ns
si no en té, escriu x=N (majúscula)

]]> 1.0000000 0.3333333 0 0 x=#r1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><msup><mi>s1</mi><mn>2</mn></msup></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi><mo>=</mo><mo>-</mo><msup><mi>s1</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>s2</mi><mo>,</mo><mi>s3</mi></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>s</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>a</mi><mo>·</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mi>a</mi><mo>*</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s</mi><mo>=</mo><mi>s2</mi></mrow><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>"</mo><mo>±</mo><mo>"</mo><mi>s1</mi></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mo>"</mo><mi>i</mi><mo> </mo><mi>traiem</mi><mo> </mo><mi>les</mi><mo> </mo><mi>dues</mi><mo> </mo><mi>arrels</mi><mo> </mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>w1</mi><mo>=</mo><mo>"</mo><mi>Té</mi><mo> </mo><mi>dues</mi><mo> </mo><mi>solucions</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w2</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>r1</mi></mtd></mtr><mtr><mtd><mi>w3</mi><mo>=</mo><mo>"</mo><mo><</mo><mn>0</mn><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mo>"</mo><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mi>no</mi><mo> </mo><mi>pot</mi><mo> </mo><mi>ser</mi><mo> </mo><mi>negatiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w1</mi><mo>=</mo><mo>"</mo><mi>No</mi><mo> </mo><mi>té</mi><mo> </mo><mi>solució</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w2</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>w3</mi><mo>=</mo><mo>"</mo><mo>></mo><mn>0</mn><mo>"</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>486</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>486</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>81</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>±</mo><mfenced><mn>9</mn></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>i</ms><mo> </mo><ms>traiem</ms><mo> </mo><ms>les</ms><mo> </mo><ms>dues</ms><mo> </mo><ms>arrels</ms><mo> </mo><mo>±</mo><mo> </mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ho resolem com un primer grau, transposant:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«/math»

]]> Com en un primer grau, dividim per #a:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»3«/mn»«/math»

]]> 4.04.2.1.12Q E2G1: Resol ax^2+c=0 SolucionsRACIONALS_2 Calculeu, si s'escau, les dues solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta:

si en té, escriu x=solució/ns
si no en té, escriu x=N (majúscula)

]]> ]]> 1.0000000 0.3333333 0 0 x=#r1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>12</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><msup><mi>s1</mi><mn>2</mn></msup></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi><mo>=</mo><mo>-</mo><msup><mi>s1</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>s2</mi><mo>,</mo><mi>s3</mi></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>s</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>a</mi><mo>·</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mi>a</mi><mo>*</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s</mi><mo>=</mo><mi>s2</mi></mrow><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>"</mo><mo>±</mo><mo>"</mo><mi>s1</mi></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mo>"</mo><mi>i</mi><mo> </mo><mi>traiem</mi><mo> </mo><mi>les</mi><mo> </mo><mi>dues</mi><mo> </mo><mi>arrels</mi><mo> </mo><mo>±</mo><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mo>"</mo><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mi>no</mi><mo> </mo><mi>pot</mi><mo> </mo><mi>ser</mi><mo> </mo><mi>negatiu</mi><mo>"</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>486</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>486</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>81</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>±</mo><mfenced><mn>9</mn></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>i</ms><mo> </mo><ms>traiem</ms><mo> </mo><ms>les</ms><mo> </mo><ms>dues</ms><mo> </mo><ms>arrels</ms><mo> </mo><mo>±</mo><mo> </mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ho resolem com un primer grau, transposant:

]]> Com en un primer grau, dividim per #a:

]]> 4.04.2.1.21Q E2G1: Resol ax^2+c=0 Sol_IRRACIONALS Calculeu, si s'escau, les dues solucions de: #e

Format de la resposta:

si en té, escriu x=solució/ns
si no en té, escriu x=N (majúscula)

LES ARRELS S'HAN DE SIMPLIFICAR

]]> ]]> 1.0000000 0.3333333 0 0 x=#r1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>99</mn><mo>)</mo></mrow><mrow><msqrt><mi>s1</mi></msqrt><mo>∉</mo><integers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>s1</mi></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi><mo>=</mo><mo>-</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>s2</mi><mo>,</mo><mi>s3</mi></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>s</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>a</mi><mo>·</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mi>a</mi><mo>*</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s</mi><mo>=</mo><mi>s2</mi></mrow><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>"</mo><mo>±</mo><mo>"</mo><msqrt><mi>s1</mi></msqrt></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mo>"</mo><mi>i</mi><mo> </mo><mi>traiem</mi><mo> </mo><mi>les</mi><mo> </mo><mi>dues</mi><mo> </mo><mi>arrels</mi><mo> </mo><mo>±</mo><mo> </mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mo>"</mo><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mi>no</mi><mo> </mo><mi>pot</mi><mo> </mo><mi>ser</mi><mo> </mo><mi>negatiu</mi><mo>"</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>288</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mo>-</mo><mn>288</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>48</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>±</mo><mfenced><mrow><mn>4</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>i</ms><mo> </mo><ms>traiem</ms><mo> </mo><ms>les</ms><mo> </mo><ms>dues</ms><mo> </mo><ms>arrels</ms><mo> </mo><mo>±</mo><mo> </mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ho resolem com un primer grau, transposant:

]]> Com en un primer grau, dividim per #a:

]]> 4.04.2.1.22Q E2G1: Resol ax^2+c=0 Sol_IRRACIONALS_2 Calculeu, si s'escau, les dues solucions de: #e

Format de la resposta:

si en té, escriu x=solució/ns
si no en té, escriu x=N (majúscula)

LES ARRELS S'HAN DE SIMPLIFICAR

]]> #w1 #r1]]> 1.0000000 0.3333333 0 0 x=#r1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>99</mn><mo>)</mo></mrow><mrow><msqrt><mi>s1</mi></msqrt><mo>∉</mo><integers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>s1</mi></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi><mo>=</mo><mo>-</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>s2</mi><mo>,</mo><mi>s3</mi></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>s</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>a</mi><mo>·</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mi>a</mi><mo>*</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s</mi><mo>=</mo><mi>s2</mi></mrow><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>"</mo><mo>±</mo><mo>"</mo><msqrt><mi>s1</mi></msqrt></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mo>"</mo><mi>i</mi><mo> </mo><mi>traiem</mi><mo> </mo><mi>les</mi><mo> </mo><mi>dues</mi><mo> </mo><mi>arrels</mi><mo> </mo><mo>±</mo><mo> </mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>w1</mi><mo>=</mo><mo>"</mo><mi>Té</mi><mo> </mo><mi>dues</mi><mo> </mo><mi>solucions</mi><mo> </mo><mi>oposades</mi><mo>:</mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mo>"</mo><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mi>no</mi><mo> </mo><mi>pot</mi><mo> </mo><mi>ser</mi><mo> </mo><mi>negatiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>w1</mi><mo>=</mo><mo>"</mo><mi>No</mi><mo> </mo><mi>té</mi><mo> </mo><mi>solució</mi><mo>"</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>18</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>±</mo><mfenced><msqrt><mn>6</mn></msqrt></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>i</ms><mo> </mo><ms>traiem</ms><mo> </mo><ms>les</ms><mo> </mo><ms>dues</ms><mo> </mo><ms>arrels</ms><mo> </mo><mo>±</mo><mo> </mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ho resolem com un primer grau, transposant:

]]> Com en un primer grau, dividim per #a:

]]> 4.04.2.1.51Q E2G1 Triar opció Les dues solucions de l'equació #e_1 són:

]]> 1.0000000 1.0000000 0 true true abc #r_11 #r_12 #r_13 #r_14 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>b</mi><mo>,</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>b</mi><mo>,</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi><mo>=</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>a</mi><mo>,</mo><mi>a</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_14</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>567</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>9</mn><mo>,</mo><mn>9</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_14</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>7</mn><mo>,</mo><mn>9</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> Si x² ≥ 0, les dues solucions de ax² + c = 0 es calculen amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#177;«/mo»«msqrt mathcolor=¨#003300¨»«mfrac»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«/msqrt»«/mrow»«/mstyle»«/math»

]]> 4.04.2.1.52Q E2G1 Triar opció_2 Les dues solucions de l'equació #e_1 són:

]]> 4t ESO/4.04 EQUACIONS/4.04.2 Equació 2n grau/4.04.2.2 E2G2: ax^2+bx=0 4.04.2.2.10 TEORIA: E2G2 ax^2+bx=0

Equació incompleta II: ax² + bx = 0

Per resoldre una equació del tipus ax² + bx = 0,

es treu factor comú:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mi»b«/mi»«mi»x«/mi»«mo»=«/mo»«mn»0«/mn»«mo»§#8660;«/mo»«mi»x«/mi»«mo»(«/mo»«mi»a«/mi»«mi»x«/mi»«mo»+«/mo»«mi»b«/mi»«mo»)«/mo»«mo»=«/mo»«mn»0«/mn»«mo»§#8660;«/mo»«mfenced open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi»x«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»a«/mi»«mi»x«/mi»«mo»+«/mo»«mi»b«/mi»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

i les solucions són x = 0 i x = -b/a

Sempre hi ha dues solucions, una d'elles és 0.

]]> 0.0000000 0.0000000 0 4.04.2.2.10_1 TEORIA E2G1: ax2+bx=0 (GIF)

]]> 0.0000000 0.0000000 0 4.04.2.2.11Q E2G2: Resol ax^2+bx=0 Calculeu les dues solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: {2,3}

]]> ]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>mínim</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>màxim</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>r1</mi><mo>,</mo><mi>r2</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>17</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>51</mn><mo>*</mo><mi>x</mi><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>51</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mo>-</mo><mn>51</mn><mo>,</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2601</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mn>17</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es treu factor comú de l'expressió:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/math»

]]> Una solució és x = 0.

L'altra es troba resolent «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/math»

]]> 4.04.2.2.12 Q E2G2: Resol ax^2+bx=0_2 Calculeu les dues solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: {2,3}

]]> Una solució és x = 0.

]]> 4.04.2.2.51Q E2G2 Tria resposta Les dues solucions de l'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«/mrow»«/mstyle»«/math»són:

]]> 1.0000000 0.1000000 0 true true abc #r_11 #r_12 #r_13 #r_14 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>a</mi><mi>b</mi></mfrac><mo>∉</mo><integers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfrac><mi>b</mi><mi>a</mi></mfrac><mo>∉</mo><integers/></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mi>x</mi><mo>*</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi><mo>/</mo><mi>a</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi><mo>=</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>b</mi><mo>/</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>/</mo><mi>a</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>/</mo><mi>b</mi><mo>,</mo><mo>-</mo><mi>a</mi><mo>/</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_14</mi><mo>=</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mo>-</mo><mi>b</mi><mo>/</mo><mi>a</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>567</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>9</mn><mo>,</mo><mn>9</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_14</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>7</mn><mo>,</mo><mn>9</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Zero sempre és solució.

L'altre solució es troba factoritzant: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mrow»«/mstyle»«/math»

I resolent: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mrow»«/mstyle»«/math»

]]> 4.04.2.2.52Q E2G2 Tria resposta_2 Les dues solucions de l'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«/mrow»«/mstyle»«/math»són:

]]> 4t ESO/4.04 EQUACIONS/4.04.2 Equació 2n grau/4.04.2.3 E2G3: ax^2+bx+c=0/4.04.2.3.1 Discriminant 4.04.2.3.1.10 TEORIA: E2G3 CÀLCUL DE DELTA

Càlcul del discriminant

El discriminant d'una equació de 2n grau,

ax² + bx + c = 0, es calcula amb:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨»§#916;«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«msup»«mi mathvariant=¨bold¨»b«/mi»«mn»2«/mn»«/msup»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«mfenced close=¨]¨ open=¨[¨»«mrow»«mn»4«/mn»«mo»·«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo»·«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/math»

b² és sempre positiu.
Cal prestar atenció en:

els signes de a i c (pel signe de 4·a·c)
el fet que 4·a·c s'ha de restar

]]> 0.0000000 0.0000000 0 4.04.2.3.1.10_1 TEORIA: E2G3 CÀLCUL DE DELTA (GIF)

]]> 0.0000000 0.0000000 0 4.04.2.3.1.11Q E2G3 Càlcul de Delta Calcula el discriminant de l'equació de 2n grau següent:

Escriu només el resultat: 36

]]> 1.0000000 0.5000000 0 0 #d_12 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq_02</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_12</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mo>-</mo><mn>60</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq_02</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#d_12</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> N'hi ha prou amb aplicar l'expressió: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«msup mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mfenced mathcolor=¨#007F00¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/math»
En aquest cas: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«msup mathcolor=¨#007F00¨»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mfenced mathcolor=¨#007F00¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»-«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«/math»

]]> 4.04.2.3.1.12Q E2G3 Càlcul de Delta_2 Calcula el discriminant de l'equació de 2n grau següent:

Escriu només el resultat: 36

]]> 4t ESO/4.04 EQUACIONS/4.04.2 Equació 2n grau/4.04.2.3 E2G3: ax^2+bx+c=0/4.04.2.3.2 Nombre de solucions 4.04.2.3.2.10 TEORIA E2G3 NOMBRE SOLUCIONS

Equació completa ax²+bx+c=0

Nombre de solucions

Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨»§#916;«/mi»«mo»§nbsp;«/mo»«mo»§gt;«/mo»«mo»§nbsp;«/mo»«mn»0«/mn»«/math», l'equació té dues solucions.

Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨»§#916;«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mn»0«/mn»«/math», l'equació té una solució doble

Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨»§#916;«/mi»«mo»§nbsp;«/mo»«mo»§lt;«/mo»«mo»§nbsp;«/mo»«mn»0«/mn»«/math», l'equació no té cap solució real

]]> 0.0000000 0.0000000 0 4.04.2.3.2.10_1 TEORIA E2G3 NOMBRE SOLUCIONS (GIF)

]]> 0.0000000 0.0000000 0 4.04.2.3.2.11Q E2G3 Nombre d solucions Determineu, calculant el discriminant, quantes solucions té l'equació:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»eq_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»02«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»0«/mn»«/mstyle»«/math»

Format de la resposta:
0 si no té solució
1 si té solució doble
2 si té dues solucions

]]> 1.0000000 0.5000000 0 0 #s_01 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq_02</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>d</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>k</mi><mo>=</mo><mo>&quot;</mo><mi>positiu</mi><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>d</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>k</mi><mo>=</mo><mo>&quot;</mo><mi>nul</mi><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>d</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>k</mi><mo>=</mo><mo>&quot;</mo><mi>negatiu</mi><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>d</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>s_01</mi><mo>=</mo><mn>2</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>d</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>s_01</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>s_01</mi><mo>=</mo><mn>0</mn></mrow></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq_02</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>216</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_01</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#s_01</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> Com que el discriminant val #d, i és #k, la resposta és evident!

]]> 4.04.2.3.2.12Q E2G3 Nombre d solucions_2 Determineu, calculant el discriminant, quantes solucions té l'equació:

Format de la resposta:
0 si no té solució
1 si té solució doble
2 si té dues solucions

]]> 4t ESO/4.04 EQUACIONS/4.04.2 Equació 2n grau/4.04.2.3 E2G3: ax^2+bx+c=0/4.04.2.3.3 Càlcul de les 2 solucions 4.04.2.3.3.10 TEORIA E2G3 CÀLCUL2SOLUCIONS

Equació de 2n grau completa
Càlcul de les 2 solucions

Quan el discriminant és positiu, es poden calcular les dues solucions amb:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨»x«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mfrac»«mrow»«mo»-«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo»±«/mo»«msqrt»«mi mathvariant=¨bold¨»§#916;«/mi»«/msqrt»«/mrow»«mrow»«mn»2«/mn»«mo»·«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/math»
La més petita s'anomena x₁ i la més gran x₂.

]]> 0.0000000 0.0000000 0 4.04.2.3.3.10_1 TEORIA E2G3 CÀLCUL2SOLUCIONS

]]> 0.0000000 0.0000000 0 4.04.2.3.3.11Q E2G3: Càlcul2SolucionsEnteres Calcula les dues solucions de:

Format de la resposta: ordenades x1 la més petita, x2 la més gran.

]]> ]]> 1.0000000 0.3333333 0 0 x1=#r_44x2=#r_45]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfenced close="|" open="|"><mi>s1</mi></mfenced><mo><</mo><mfenced close="|" open="|"><mi>s2</mi></mfenced></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>s1</mi><mo><</mo><mi>s2</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_44</mi><mo>=</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_45</mi><mo>=</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>13</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>50</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>312</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mn>50</mn><mo>,</mo><mn>312</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_44</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_45</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mn>1</mn><mo>=</mo><mo>#</mo><mi>r</mi><mi>_</mi><mn>44</mn><mspace linebreak="newline"/><mi>x</mi><mn>2</mn><mo>=</mo><mo>#</mo><mi>r</mi><mi>_</mi><mn>45</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«/mstyle»«/math»

]]> Les solucions es calculen amb:

]]> 4.04.2.3.3.12Q E2G3: Càlcul2SolucionsEnteres_2 Calcula les dues solucions de:

Format de la resposta: ordenades x1 la més petita, x2 la més gran.

]]> ]]> 1.0000000 0.3333333 0 0 x1=#r_44x2=#r_45]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfenced close="|" open="|"><mi>s1</mi></mfenced><mo><</mo><mfenced close="|" open="|"><mi>s2</mi></mfenced></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>s1</mi><mo><</mo><mi>s2</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_44</mi><mo>=</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_45</mi><mo>=</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mn>12</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>49</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_44</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_45</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mn>1</mn><mo>=</mo><mo>#</mo><mi>r</mi><mi>_</mi><mn>44</mn><mspace linebreak="newline"/><mi>x</mi><mn>2</mn><mo>=</mo><mo>#</mo><mi>r</mi><mi>_</mi><mn>45</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«/mstyle»«/math»

]]> Les solucions es calculen amb:

]]> 4.04.2.3.3.21Q E2G3: Càlcul2SolucionsRacionals Calcula les dues solucions de:

Format de la resposta: {x=1/2,x=3/4}

]]> ]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>d11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>d11</mi></mfrac></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>a5</mi><mo>*</mo><mi>d11</mi></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>s1</mi><mo>∉</mo><integers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>d</mi><mo>∈</mo><integers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfenced close="|" open="|"><mi>b</mi></mfenced><mo><</mo><mn>50</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>d</mi><mo>></mo><mn>0</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mi>s1</mi><mo>,</mo><mi>x</mi><mo>=</mo><mi>s2</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>,</mo><mo>-</mo><mfrac><mn>3</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>,</mo><mn>24</mn><mo>,</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mn>3</mn><mn>5</mn></mfrac><mo>,</mo><mi>x</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«/mstyle»«/math»

]]> Les solucions es calculen amb:

]]> 4.04.2.3.3.22Q E2G3: Càlcul2SolucionsRacionals_2 Calcula les dues solucions de:

Format de la resposta: {x=1/2,x=3/4}

]]> ]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>d11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>d11</mi></mfrac></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>a5</mi><mo>*</mo><mi>d11</mi></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>s1</mi><mo>∉</mo><integers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>d</mi><mo>∈</mo><integers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfenced close="|" open="|"><mi>b</mi></mfenced><mo><</mo><mn>50</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>d</mi><mo>></mo><mn>0</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mi>s1</mi><mo>,</mo><mi>x</mi><mo>=</mo><mi>s2</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>,</mo><mo>-</mo><mfrac><mn>3</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>,</mo><mn>24</mn><mo>,</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mn>3</mn><mn>5</mn></mfrac><mo>,</mo><mi>x</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«/mstyle»«/math»

]]> Les solucions es calculen amb:

]]> 4.04.2.3.3.31Q E2G3: Càlcul2SolucionsIRRacionals Calcula, si s'escau, les dues solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»e«/mi»«/math»

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨]¨ open=¨[¨»«mrow»«mfrac»«mrow»«mo»-«/mo»«mn»3«/mn»«mo»-«/mo»«msqrt»«mn»15«/mn»«/msqrt»«/mrow»«mn»4«/mn»«/mfrac»«mo»,«/mo»«mfrac»«mrow»«mo»-«/mo»«mn»3«/mn»«mo»+«/mo»«msqrt»«mn»15«/mn»«/msqrt»«/mrow»«mn»4«/mn»«/mfrac»«/mrow»«/mfenced»«/math»amb denominador positiu, i l'arrel simplificada.

]]> ]]> 1.0000000 0.3333333 0 0 #r_44]]> #r_45]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>D</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>D</mi><mo>></mo><mn>0</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><msqrt><mi>D</mi></msqrt></mtd></mtr></mtable><mfenced><mrow><mi>d</mi><mo>∉</mo><rationals/></mrow></mfenced></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_44</mi><mo>=</mo><mfenced close="]" open="["><mrow><mfrac><mrow><mo>-</mo><mi>b</mi><mo>-</mo><msqrt><mi>D</mi></msqrt></mrow><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>-</mo><mi>b</mi><mo>+</mo><msqrt><mi>D</mi></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_45</mi><mo>=</mo><mfenced close="]" open="["><mrow><mfrac><mrow><mo>-</mo><mi>b</mi><mo>+</mo><msqrt><mi>D</mi></msqrt></mrow><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>-</mo><mi>b</mi><mo>-</mo><msqrt><mi>D</mi></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D1</mi><mo>=</mo><msqrt><mi>D</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>73</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_44</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><msqrt><mn>73</mn></msqrt><mn>6</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><msqrt><mn>73</mn></msqrt><mn>6</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_45</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mfrac><msqrt><mn>73</mn></msqrt><mn>6</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><msqrt><mn>73</mn></msqrt><mn>6</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>44</mn></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>45</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic" correctAnswer="1"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«msup mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»D«/mi»«/mstyle»«/math»

]]> Les solucions es calculen amb

]]> 4.04.2.3.3.32Q E2G3: Càlcul2SolucionsIRRacionals_2 Calcula, si s'escau, les dues solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»e«/mi»«/math»

]]> ]]> 1.0000000 0.3333333 0 0 #r_44]]> #r_45]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>D</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>D</mi><mo>></mo><mn>0</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><msqrt><mi>D</mi></msqrt></mtd></mtr></mtable><mfenced><mrow><mi>d</mi><mo>∉</mo><rationals/></mrow></mfenced></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_44</mi><mo>=</mo><mfenced close="]" open="["><mrow><mfrac><mrow><mo>-</mo><mi>b</mi><mo>-</mo><msqrt><mi>D</mi></msqrt></mrow><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>-</mo><mi>b</mi><mo>+</mo><msqrt><mi>D</mi></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_45</mi><mo>=</mo><mfenced close="]" open="["><mrow><mfrac><mrow><mo>-</mo><mi>b</mi><mo>+</mo><msqrt><mi>D</mi></msqrt></mrow><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>-</mo><mi>b</mi><mo>-</mo><msqrt><mi>D</mi></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D1</mi><mo>=</mo><msqrt><mi>D</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>73</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_44</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><msqrt><mn>73</mn></msqrt><mn>6</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><msqrt><mn>73</mn></msqrt><mn>6</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_45</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mfrac><msqrt><mn>73</mn></msqrt><mn>6</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><msqrt><mn>73</mn></msqrt><mn>6</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>44</mn></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>45</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic" correctAnswer="1"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«msup mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»D«/mi»«/mstyle»«/math»

]]> Les solucions es calculen amb

]]> 4.04.2.3.3.41Q E2G3: Càlcul2SolucionsVariable m Calcula les dues solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: ordenades m1 la més petita,m2 la més gran.

]]> ]]> 1.0000000 0.3333333 0 0 m1=#r_44m2=#r_45]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfenced close="|" open="|"><mi>s1</mi></mfenced><mo><</mo><mfenced close="|" open="|"><mi>s2</mi></mfenced><mo>+</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>s1</mi><mo><</mo><mi>s2</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>m</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>m</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_44</mi><mo>=</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_45</mi><mo>=</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>19</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>m</mi><mn>2</mn></msup><mo>+</mo><mn>48</mn><mo>*</mo><mi>m</mi><mo>-</mo><mn>190</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mn>48</mn><mo>,</mo><mo>-</mo><mn>190</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>784</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_44</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_45</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mn>1</mn><mo>=</mo><mo>#</mo><mi>r</mi><mi>_</mi><mn>44</mn><mspace linebreak="newline"/><mi>m</mi><mn>2</mn><mo>=</mo><mo>#</mo><mi>r</mi><mi>_</mi><mn>45</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»d«/mi»«/mstyle»«/math»

]]> Les solucions es calculen amb:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/msqrt»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 4.04.2.3.3.42Q E2G3: Càlcul2SolucionsVariable t Calcula les dues solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mstyle»«/math»

Format de la resposta: ordenades t1 la més petita, t2 la més gran.

]]> ]]> 1.0000000 0.3333333 0 0 t1=#r_44t2=#r_45]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfenced close="|" open="|"><mi>s1</mi></mfenced><mo><</mo><mfenced close="|" open="|"><mi>s2</mi></mfenced></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>s1</mi><mo><</mo><mi>s2</mi></mrow></mfenced><mo> </mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>t</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>t</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_44</mi><mo>=</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_45</mi><mo>=</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mn>39</mn><mo>*</mo><mi>t</mi><mo>+</mo><mn>42</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>39</mn><mo>,</mo><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2025</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_44</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_45</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mn>1</mn><mo>=</mo><mo>#</mo><mi>r</mi><mi>_</mi><mn>44</mn><mspace linebreak="newline"/><mi>t</mi><mn>2</mn><mo>=</mo><mo>#</mo><mi>r</mi><mi>_</mi><mn>45</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»d«/mi»«/mstyle»«/math»

]]> Les solucions es calculen amb:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/msqrt»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 4.04.2.3.3.51Q E2G3 Tria resposta Les dues solucions de l'equació #e_1 són:

]]> 1.0000000 0.5000000 0 true true abc #r_11 #r_12 #r_13 #r_14 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mfenced><mrow><mi>s1</mi><mo>+</mo><mi>s2</mi></mrow></mfenced><mo>*</mo><mi>a</mi></mtd></mtr></mtable><mrow><mfenced><mrow><mi>s1</mi><mo>≠</mo><mi>s2</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfenced close="|" open="|"><mi>b</mi></mfenced><mo>></mo><mn>100</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mo>{</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi><mo>=</mo><mo>{</mo><mo>-</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi><mo>=</mo><mo>{</mo><mo>-</mo><mi>s1</mi><mo>,</mo><mo>-</mo><mi>s2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_14</mi><mo>=</mo><mo>{</mo><mi>s1</mi><mo>,</mo><mo>-</mo><mi>s2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>s1</mi><mo>*</mo><mi>s2</mi><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>145</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1020</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>17</mn><mo>,</mo><mn>12</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>17</mn><mo>,</mo><mn>12</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>17</mn><mo>,</mo><mo>-</mo><mn>12</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_14</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>17</mn><mo>,</mo><mo>-</mo><mn>12</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>,</mo><mn>145</mn><mo>,</mo><mo>-</mo><mn>1020</mn><mo>,</mo><mn>625</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> El discriminant és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«/mrow»«/mstyle»«/math»

]]> 4.04.2.3.3.52Q E2G3 Tria resposta_2 Les dues solucions de l'equació #e_1 són:

]]> 1.0000000 0.5000000 0 true true abc #r_11 #r_12 #r_13 #r_14 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>s1</mi><mo>+</mo><mi>s2</mi></mrow></mfenced><mo>*</mo><mi>a</mi></mtd></mtr></mtable><mrow><mfenced><mrow><mi>s1</mi><mo>≠</mo><mi>s2</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfenced close="|" open="|"><mi>b</mi></mfenced><mo>></mo><mn>100</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mo>{</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi><mo>=</mo><mo>{</mo><mo>-</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi><mo>=</mo><mo>{</mo><mo>-</mo><mi>s1</mi><mo>,</mo><mo>-</mo><mi>s2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_14</mi><mo>=</mo><mo>{</mo><mi>s1</mi><mo>,</mo><mo>-</mo><mi>s2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>s1</mi><mo>*</mo><mi>s2</mi><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>160</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1260</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>14</mn><mo>,</mo><mn>18</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>14</mn><mo>,</mo><mn>18</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>14</mn><mo>,</mo><mo>-</mo><mn>18</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_14</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>14</mn><mo>,</mo><mo>-</mo><mn>18</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>,</mo><mn>160</mn><mo>,</mo><mo>-</mo><mn>1260</mn><mo>,</mo><mn>400</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> El discriminant és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«/mrow»«/mstyle»«/math»

]]> 4t ESO/4.04 EQUACIONS/4.04.2 Equació 2n grau/4.04.2.3 E2G3: ax^2+bx+c=0/4.04.2.3.4 Càlcul de la solució doble 4.04.2.3.4.10 TEORIA: E2G3 SOLUCIÓ DOBLE

Equació de 2n grau completa

Solució doble

Si el discriminant de l'equació és 0,

aleshores les dues solucions són iguals.

Aquesta solució doble es calcula amb:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn»2«/mn»«/msub»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mo»-«/mo»«mfrac»«mi mathvariant=¨bold¨»b«/mi»«mrow»«mn»2«/mn»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/math»

]]> 0.0000000 0.0000000 0 4.04.2.3.4.10_1 TEORIA: E2G3 SOLUCIÓ DOBLE (GIF)

]]> 0.0000000 0.0000000 0 4.04.2.3.4.11Q E2G3: CàlculSolucióDobleEntera Calcula, si s'escau, les solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: x = 3

]]> ]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>s1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>64</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mo>-</mo><mn>16</mn><mo>,</mo><mn>64</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mstyle»«/math»

]]> Com que el discriminant és zero, la solució doble es calcula amb:

]]> 4.04.2.3.4.12Q E2G3: CàlculSolucióDobleEntera_2 Calcula, si s'escau, les solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: x = 3

]]> Com que el discriminant és zero, la solució doble es calcula amb:

]]> 4.04.2.3.4.21Q E2G3: CàlculSolucióDobleRacional Calcula, si s'escau, les solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: x = 2/3 (SIMPLIFICADA)

]]> ]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>n2</mi></mfrac></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>a5</mi><mo>*</mo><msup><mfenced><mi>n2</mi></mfenced><mn>2</mn></msup></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>s1</mi><mo>∉</mo><integers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfenced close="|" open="|"><mi>a</mi></mfenced><mo><</mo><mn>26</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>s1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>18</mn><mo>,</mo><mfrac><mn>8</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>18</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>96</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>128</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>18</mn><mo>,</mo><mn>96</mn><mo>,</mo><mo>-</mo><mn>128</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mfrac><mn>8</mn><mn>3</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mstyle»«/math»

]]> Com que el discriminant és zero, la solució doble es calcula amb:

]]> 4.04.2.3.4.22Q E2G3: CàlculSolucióDobleRacional_2 Calcula, si s'escau, les solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: x = 2/3 (SIMPLIFICADA)

]]> ]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>n2</mi></mfrac></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>a5</mi><mo>*</mo><msup><mfenced><mi>n2</mi></mfenced><mn>2</mn></msup></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>s1</mi><mo>∉</mo><integers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfenced close="|" open="|"><mi>a</mi></mfenced><mo><</mo><mn>26</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>s1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>,</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mstyle»«/math»

]]> Com que el discriminant és zero, la solució doble es calcula amb:

]]> 4.04.2.3.4.31Q E2G3: CàlculSolucióDobleIRRRacional Calcula, si s'escau, les solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: x = 2/3 (SIMPLIFICADA)

]]> ]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><msqrt><mi>r1</mi></msqrt></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mi>s1</mi><mo>∉</mo><rationals/></mrow></mfenced></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>s1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>12</mn><mo>*</mo><msqrt><mn>3</mn></msqrt><mo>*</mo><mi>x</mi><mo>+</mo><mn>36</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mo>-</mo><mn>12</mn><mo>*</mo><msqrt><mn>3</mn></msqrt><mo>,</mo><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mstyle»«/math»

]]> Com que el discriminant és zero, la solució doble es calcula amb:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

Si es pot cal simplificar

]]> 4.04.2.3.4.32Q E2G3: CàlculSolucióDobleIRRRacional_2 Calcula, si s'escau, les solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: x = 2/3 (SIMPLIFICADA)

]]> ]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><msqrt><mi>r1</mi></msqrt></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mi>s1</mi><mo>∉</mo><rationals/></mrow></mfenced></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>s1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>12</mn><mo>*</mo><msqrt><mn>3</mn></msqrt><mo>*</mo><mi>x</mi><mo>+</mo><mn>36</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mo>-</mo><mn>12</mn><mo>*</mo><msqrt><mn>3</mn></msqrt><mo>,</mo><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mstyle»«/math»

]]> Com que el discriminant és zero, la solució doble es calcula amb:

Si es pot cal simplificar

]]> 4.04.4.51C E2G3 Tria resposta La solució doble de l'equació #e_1 és:

]]> 1.0000000 1.0000000 0 true true abc #r_11 #r_12 #r_13 #r_14 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi><mo>=</mo><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_14</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>80</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>400</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_14</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> 4.04.4.52C E2G3 Tria resposta_2 La solució doble de l'equació #e_1 és:

]]> 1.0000000 1.0000000 0 true true abc #r_11 #r_12 #r_13 #r_14 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi><mo>=</mo><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_14</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>80</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>400</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_14</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> 4t ESO/4.04 EQUACIONS/4.04.2 Equació 2n grau/4.04.2.3 E2G3: ax^2+bx+c=0/4.04.2.3.5 Comprovació S i P 4.04.2.3.5.10 TEORIA: Suma i Producte

Suma i producte de les solucions

Quan l'equació de 2n grau té duessolucions: x₁ i x₂ o una doble x₁ = x₂,

la suma de les solucions és igual a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨»S«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mo»-«/mo»«mfrac»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«/math»
el producte de les solucions és igual a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨»P«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mfrac»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«/math»

]]> 0.0000000 0.0000000 0 4.04.2.3.5.11Q E2G3: Calcular S i P sense resoldre Calcula, SENSE RESOLDRE L'EQUACIÓ, la suma i el producte de les solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

]]> ]]> 1.0000000 0.5000000 0 0 Suma=#SProducte=#P]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced close="|" open="|"><mi>s1</mi></mfenced><mo><</mo><mfenced close="|" open="|"><mi>s2</mi></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>s1</mi><mo>,</mo><mi>s2</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>s1</mi><mo>+</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mn>17</mn><mo>,</mo><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>38</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>68</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>38</mn><mo>,</mo><mn>68</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>900</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>,</mo><mi>d1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mo>-</mo><mn>38</mn><mo>,</mo><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>17</mn><mo>,</mo><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>19</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>34</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mi>u</mi><mi>m</mi><mi>a</mi><mo>=</mo><mo>#</mo><mi>S</mi><mspace linebreak="newline"/><mi>P</mi><mi>r</mi><mi>o</mi><mi mathvariant="normal">d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>P</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La suma és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»S«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«/math» i el producte «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«/math»

]]> 4.04.2.3.5.12Q E2G3: IntuirSolucionsambSiP a) Calcula, SENSE RESOLDRE L'EQUACIÓ, la suma i el producte de les solucions de:

b) Intueix quines són les solucions (Format: {1,3})

]]> ]]> 1.0000000 0.5000000 0 0 Suma=#SProducte=#PSolucions=#sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mi>s1</mi><mo>+</mo><mi>s2</mi></mtd></mtr><mtr><mtd><mi>P</mi><mo>=</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></mtd></mtr><mtr><mtd><mi>w1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>P</mi></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>ordena</mi><mfenced><mrow><mi>divisors</mi><mo>(</mo><mi>P</mi><mo>)</mo></mrow></mfenced></mtd></mtr></mtable><mrow><mfenced><mrow><mfenced close="|" open="|"><mi>s1</mi></mfenced><mo><</mo><mfenced close="|" open="|"><mi>s2</mi></mfenced></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfenced close="|" open="|"><mrow><mi>a</mi><mo>*</mo><mi>P</mi></mrow></mfenced><mo><</mo><mn>60</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo><mo>≠</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>longitud</mi><mo>(</mo><mi>sol2</mi><mo>)</mo><mo><</mo><mn>7</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>longitud</mi><mfenced><mi>sol2</mi></mfenced><mo>></mo><mn>4</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>s1</mi><mo>,</mo><mi>s2</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>s1</mi><mo>,</mo><mi>s2</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>18</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>32</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mn>18</mn><mo>,</mo><mo>-</mo><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>196</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>,</mo><mi>d1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>18</mn><mo>,</mo><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>16</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>16</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>16</mn><mo>,</mo><mn>32</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mi>u</mi><mi>m</mi><mi>a</mi><mo>=</mo><mo>#</mo><mi>S</mi><mspace linebreak="newline"/><mi>P</mi><mi>r</mi><mi>o</mi><mi mathvariant="normal">d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>P</mi><mspace linebreak="newline"/><mi>S</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La suma és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»S«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«/mstyle»«/math» i el producte «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«/mstyle»«/math»

]]> Per deduir les solucions, cal pensar que les dues són divisors del producte.

Els divisors naturals de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mrow»«/mstyle»«/math» són «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mrow»«/mstyle»«/math»

Per tempteig i jugant amb la suma (la suma dels dos nombres és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»S«/mi»«/mrow»«/mstyle»«/math») i els signes, es poden deduir.

]]> 4.04.2.3.5.21Q E2G3: 2 Solucions + S + P a) Calcula, si s'escau les solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

b) Calcula'n la suma i el producte

Format de la resposta:

Solucions ={x₁,x₂}

Suma=

Producte=

]]> ]]> 1.0000000 0.5000000 0 0 Solucions=#w1Suma=#SProducte=#P]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced close="|" open="|"><mi>s1</mi></mfenced><mo><</mo><mfenced close="|" open="|"><mi>s2</mi></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>s1</mi><mo>,</mo><mi>s2</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>s1</mi><mo>+</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mn>17</mn><mo>,</mo><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>38</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>68</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>38</mn><mo>,</mo><mn>68</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>900</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>,</mo><mi>d1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mo>-</mo><mn>38</mn><mo>,</mo><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>17</mn><mo>,</mo><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>19</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>34</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>#</mo><mi>w</mi><mn>1</mn><mspace linebreak="newline"/><mi>S</mi><mi>u</mi><mi>m</mi><mi>a</mi><mo>=</mo><mo>#</mo><mi>S</mi><mspace linebreak="newline"/><mi>P</mi><mi>r</mi><mi>o</mi><mi mathvariant="normal">d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>P</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant es calcula amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«/mrow»«/mstyle»«/math»

i les solucions amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/msqrt»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

La suma amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»S«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«/mrow»«/mstyle»«/math» i el producte amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 4.04.2.3.5.22Q E2G3: 2 Solucions + S + P_2 a) Calcula, si s'escau les solucions de: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

b) Calcula'n la suma i el producte

Format de la resposta:

Solucions ={x₁,x₂}

Suma=

Producte=

]]> 4.04.2.3.5.51Q E2G3: EscriuEquació amb S i P Escriu una equació de segon grau tal que a = 1, que la suma de les solucions sigui «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»S«/mi»«/mstyle»«/math» i el seu producte «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»P«/mi»«/mrow»«/mstyle»«/math»

]]> ]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced close="|" open="|"><mi>s1</mi></mfenced><mo><</mo><mfenced close="|" open="|"><mi>s2</mi></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>s1</mi><mo>,</mo><mi>s2</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>s1</mi><mo>+</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>15</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>,</mo><mi>d1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que a = 1, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»S«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«/mstyle»«/math»

]]> 4t ESO/4.04 EQUACIONS/4.04.2 Equació 2n grau/4.04.2.3 E2G3: ax^2+bx+c=0/4.04.2.3.6 Altres situacions 4.04.2.3.6.10 TEORIA: Factoritzar si grau sup a 2

Equació de grau superior a 2
Sense terme independent

Si l'equació és de grau superior a 2, i NO TÉ TERME INDEPENDENT, es pot treure x elevat al grau mínim en factor comú, i intentar resoldre.

Exemple:
2x⁴ - 10x³ + 12x² = x² · (2x² - 10x + 12)
Una solució sempre és 0.
Les altres, si existeixen es troben resolent 2x² - 10x + 12 = 0.
En aquest cas, les 3 solucions són 0, 2 i 3.

]]> 0.0000000 0.0000000 0 4.04.2.3.6.11Q Resol equació grau 3 (x en factor) Escriu, ORDENADES DE MÉS PETITA A MÉS GRAN, les solucions de:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

Format: {-1,2,3}

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>x1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>x2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mo>(</mo><mi>x1</mi><mo>+</mo><mi>x2</mi><mo>)</mo><mo>*</mo><mi>a</mi></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x1</mi><mo>*</mo><mi>x2</mi></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>x1</mi><mo>≠</mo><mi>x2</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfenced close="|" open="|"><mi>c</mi></mfenced><mo><</mo><mn>50</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>ordena</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x1</mi><mo>+</mo><mi>x2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x1</mi><mo>*</mo><mi>x2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>12</mn><mo>*</mo><mi>x</mi><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>6</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>196</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>

Cal treure x en factor i et queda:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mstyle»«/math»

x=0 és una solució
troba les altres solucions amb l'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mrow»«/mstyle»«/math»

]]> 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 El determinant de l'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mrow»«/mstyle»«/math» és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«/mrow»«/mstyle»«/math»

]]> 4.04.2.3.6.12Q Resol equació grau 4 (x^2 en factor) Escriu, ORDENADES DE MÉS PETITA A MÉS GRAN, les solucions de:

Format: {-1,2,3}

Cal treure x² en factor i et queda:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mstyle»«/math»

x=0 és una solució
les altres dues solucions es troben resolent l'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mrow»«/mstyle»«/math»

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 El discriminant de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mrow»«/mstyle»«/math» és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«/mrow»«/mstyle»«/math»

]]> 4.04.2.3.6.13Q Resol grau qualsevol (x^n en factor) Escriu, ORDENADES DE MÉS PETITA A MÉS GRAN, les solucions de:

Format: {-1,2,3}

Cal treure «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/msup»«/mstyle»«/math» en factor i et queda:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»n«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mstyle»«/math»

x=0 és una solució
les altres dues solucions es troben resolent l'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mrow»«/mstyle»«/math»

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ioADJvQHRF8dKJZ5ZDX4xx8qGrSFhi4NJtZP5kH0UVEdWkSFIRIWOZ9zccVFTSwf0QjkRX8U8hBPU04JHlmxoFTUj0EepAIgqZRpklbzJSmXMxQ5WCNDTyInEUcYPjWcQ4YUAgiaOnVJJE9v0gcLnTOi2dVKhuLYXqIZwZIlhz9K5UEVf7SYEaIlTVTnFoRqWkUhhyZaE1QOCVr9qqYebJFKlKA+ZSaNaa4EyCtu8smjkillCitBnVLVlJgbwTJorivBUNpPcHWkSipbGDesQNNBmxmGsAh4bUGAGEtinNU4U4i13/7B57jzOQQIs4W2NO5hcRWF7rVVqHVkYrFsUde3BAm27WFaFQVwQZeF1RdU8B4l8GPOodQwWkaSJ5wq936bMIImfjTxSg8rrB3GBxO08bYRk1wythWjrFEsf63MMn/RopTxtdTFNxbMVsjsATXQWuzUM6vcPKwggQTCSjVC+2QFF4H0LLM1STOnVzSysBIIIqZE7XMg1rBC2wp6rQBFDFAEwoUVz/hcjRWs/KYaK4IAYsU/1aKs4LNbgQBi9T+HJJ20FdXsvYogvNE2CyulVG2N1CvDFMg/rTAHTStaR02421dUtxc0iw8ONuQlU5202NjJxMUeh0BhjdtLo05b2IKP7rMVVO8Fk2pOs1LFP3vfDXblvlWeuR64k36wFVXjnRorWgPVhfIlgz251Zl3ocfrPnug9PXPQw821dRXr5fsYkOPNPPdF7SC0oKgrnUVLLRv//0rBQQAIfkECQoAHgAsAAAAADIASwAACP0APQgcSLCgwYMIEypcWHAaNYcQp6ViSJGiQ2oPMWbMKLGiR4IXNYoc6fDVxI8MQ4qsppHlyIev/qBMONIly2o4X3KcVmimwZUYc96kJvTltGY9fQoMeVOoU6JDRR5NOvPlUJxYoWp1qVGin5mvLjbF6pSsTanUTGpBWROq2bdbScb8qHLs26xmiXbFmOprRaBl7+LVy3XatLkWxboVzFjvyFSp1jJsa9estbw5HRvmKTNly8VkL18mG5erxld+FabKeNVytX//RsM1DTPVH8kJUzEFTRa27KJnOaYq1DnhK8p3rf3G/NJk5IW6PwduDBwt6uIIjwNmfJcwWsiF/VIjXO2wKW/qjjFeNPkH+8HogM+Trt7V+e2FheoSrsxStveRzcASnnsG+QGRdOZZdtl/Ir0Ci21/iHdQFfB9thVwVxkl0YC45aYdUFpd+F9hD0IIBkV/hLWbY/Sl1xUszrxCnB8EHkRFhfF5R9te9hWiRY0H/RGdSiBaKBUs1IB3G5A2FhLWRjrtyKOS7Um4kBapPKmfTtapMtySVjIkpJZc6lQSlREqNeZFB5ZZUol/zKiUB1gOWaZ6GL3iDJVaUOXTjU/eOWUhMzLp0ZpEGpWWKq+MEucWcxaUH553XjTcFmGq+WFQDL7YF6SREkSFYdLpKBJkW+ARakGrcdr9mmnTCJjpnK26itWChY0C6qoDFVLqfA0WoiqvA/1RXlB4RfXQH7sSu4VYrwYXExXEEnScTZhxhVi1ArE2Voga2cbtQLUGxmmezVaL4Ld6TaPKrJGW61ZcfKVLrHYJFhWuvbyq0lJ3LsU67Lj4LjavS6nwu6q/tsJV77jdyqcvNapUAbEHyHLHEiykAHJxICD/w501VuxxyBMX/xMybCzDBs0spRxiCiKAXHExIP+w0vI/K8AmwxM/B6KHDNVcbA0ggry2M2ysBLIHF7GtYLTKgUCzNNUgB1KFNRdXE8gq1lwdDSuHhEyy0dYI8s8sS8sydtYrcA2x18pZ3bLOTXoHYkUgZ0NsTdZs+wZbNcpZAYjeco/7999X5wzyFXxbcbEVjA8em2/K/Y240VcwrjPL0cySNyCUSw7x3oEMHjbTTcfmtekfV74zNHlvfrEHgbCi++WwydLKKnynDfvFerBtd845s4LIHobfXhALIO/+dhUsOG/99SgFBAAh+QQJCgAeACwAAAAAMgBLAAAI/QA9CBxIsKDBgwgTKlxYcJrDhw5fMZw4ESK1aRchRqTIkaDDi9RAisQIMVXHihhBplwZkuTDV4ROJiQpMmRLmzRdTjMps+FHnDaBBs34MGZPgT9rDh2akyhPmR9TLp0aNOc0VIWg0qRqsxpXoju1nNw61Cs1s1O3QkTV8SFXtF7RLnX5KpUfjk276g0q96bKaa/uVlRJFe5Zrjp3Cl6YlG9Is3L7So3qKpVYhlGnQj7ct+rfaa7+MEzl9mu1f//iPp4LNhWhxQhf/ZTK+TBqa19ZOnQtWqFb2o6rCa+dlmhdVJcTyla61zFiwoD99E5ImuzSvp0nk0yVqhDsgxb9gV/P/bmun+8GUZGV2vkwVasw/6AvWOj3W77Z/9b1Ph0hocziTWUNbjdZBRgqfxCSHEJ4yGbdV0IV+FB35/WHUHUuMffcSh+9gqB8E/kRnl/PSXhRXQlKN5EW6gE4EmtNRcRdIVqAONEfDuZF23r6pYKVdPMhxGKOfxEGHVh1UbiFihxtgQqRasWY0YkzymdjR3+0+JuUiSXpnXdBMkRIKjlmaGZUryRJyB81HuUBHv8t56KBgM0IZFZu+lGfRkdGBVgzhfAXJkd+QMklRq80s4gobBrl5kBkzvmijPw9WpCID/YJ2ChhDHqSFqUBN1lGlVpKEGkauqeSeaYWVP2dhrhxOM2arRJUX6qe7WRZrQP90VhxJBVCBa8CiYhrVYCxSSxSAcLo6VEsvZdRd8sK5KBzTFETWLUeNJvtThbWei2Euy3IayoksnZiHtyO2xxOYXHbDIRApRJuq3LWpppKu1a7l2r7hpSKFdyOty9ahrBbbSAMpwawe9ZYoQcrMnBrTSCCoKaxxta0soogrCCiB8ELW8MKaq2gtgJqLFTRciB7yFANt9UwfNrGGrPCsBWprWDxxYGkjPM/DAdyRSBWzFztxaYMOPQ/rOgMyD8R0/zPIbfhzEorOjO8gtLLRjxgNFpDvXMgVS9dtCwco1aNNdVcAQjS1li8islPYnNdNNokL2vFxf+QfZo1txEe9yp/W3wF4Cej1njXdPdNrBUNU+001DoPWM0eki+LdiBPm93FHlzUza0HgURN9cZRZ35x556f3DjUmJeCdCCnF7RC6qu0QrjOMjyR+/DEnxQQACH5BAkKAB4ALAAAAAAyAEsAAAj9AD0IHEiwoMGDCBMqXFhQmsOHDxlKlChtWsWL0yxajDix40CIGzVexOjQI0WNIlOO3OgQlcmEJEmqzCjT5cuGDmdWVCmz5c2POzHSDCk0pkWbL4PuTJmRp1NphJKGnKlz6MqHfkzKRIlyadCnrpCevDq0q1mjOV1lnZjz61ezXIuOjDqW6lK4RYlOC7t2Ydu4VpuWJdtWWqq+Cnsy9bo4MEtUdBNXFZzR2j9qjM9iVIv4YOHBKf9dtkvYFaHOBh+CZko5c8yKkFE3fNq6qVu9JGP73brVrm2iDl+h8hMZIW7XZQfnrchXNkFXhBsvdpsbFRjnA1Gp7r2YGuiYrv1SncYuEBVuvUypeT9/sTl5D37+/vX9naU0yH9OM4S+XDFaoq+ENZ5EhAB31mSEoXKYH+8J5Id5n8mn02sCEsfgRKjw519VVwnnSn4XTqSFduxxKJI0rzATmx/5efSgKyWOdJU0MFbohxYNGkRIhttJiNZ9qBTCYIgv7Xjihm2FFR6D+v30oHZInmiRcKcR8ocWPwk04iuF9aiaRQKOl+NChDADo49WwfaKKDeOyRCUPckY0opZ6uibUhstWVyd8EWHZ1qo4MgnThumOU2Tgw4EXVXVSMlXogRBCNhtDgkJ6UDxIZgSKoFe6mBe9VV0o6cCSbmcRqaRKlBOgVHn/ZCbHkkZ6l6wdvQlkhVhqeqirBk1nKoenBrnNLqSyuVUkx5VK1tGTUcrsGfutF5G01rETLGeNjWtd+ttW0gewFKrrbjdZpTKFsAKEkgg0TQ6TbneWXOFFaZYAaw1gRwi2r78ssKKIKuwEoi9qu5hjSmizSLaCgtbsUIVgVxRRTXAVrMHItXw2++6V/xjzQr34huIxvsesi4gA1OsajWBsGKNZRqzEs26I1tDMKkvj9wKzP0KHHEV1lR8xcsk/+NvIIBcAYjN99LMyr6Wvfyy0oIA3XQ1T5Nsjc/rMq2qFfjumzHPUlvBCtj3Dh2INa30azTSA3tNqhXriia1aEc5W0bNvMAKtPbIJLfCNdp9t1wzv1sLnPPNwO7hcdt4tyL4KvMG0ndBLADCiimyeCywFVVcLvroJgUEACH5BAkKAB4ALAAAAAAyAEsAAAj9AD0IHEiwoMGDCBMqXFhQmsOHDxlKlAixosWJGAla3HgxI0OOICui8pgwpMmHrkgaPMlSWkqVAlu2HKlSpkxCJG3a9ONRZ0tXNCf6lOmKp9ChLXFSRDrT6EKmTZdCNYlKqUKb1v7pdFXUKUKs/6bpZEbI60GbYn26Kvt0qkmufsyudEuV7VW6IIHGbYt3Y9W9Cl0NnZY2JFBUfqwiRDW4cEhCZeUW9NO34uG4kgsKruwQVVG7CxlzdpkY8EI/m/FejqtloqjUbvUS0pL5oB/PsVH9xZzxdu7IoDESEj30MOKyrVUOhy3T8+7aDG8zZ8kVsR/ayWFqIf5Tmm7Ipv1hehi+dbdi8R6mn9yNviD3n6JotyeoRe3f+RpDOn4YHL9JahbphR9B77HU33yE+HRge5TZ5Ep8A+Zn03kD6lRVhBLKBJ14W20Ik08e1uRgiCSpBxJiGA7UYYoxVUSYNITFiBKJHokV44s2wnhjKlWw6IGOOd54I4yp/OGjIIEEMks1QgJpzRVWBGKFj9YEUso/WGaJZTSymMJKIKtI6eMV1iCi5T8rYBkDFDGsEMgeMlTjYzVdlGJNVmf+8+UegfxTzQpUVtlnnqx8KaWUcrJozSqC4Elokn1aMyWL1fwTaStnsiKLoYGsYA2VVtyJqZas6JlklJJSmSQgWuJZaM2dUUr5qaKBVFNqntFwGkiqLFphaZavZnknrKuECmqV1oz6D5emnsprirFiGWxWhTZqTTVi+ujBroOe2UqYzmq77ZdYOqrnl3dmq+0VWN6q57msWBGluAS5yYogspwrJaD09uuvRAEBACH5BAkKAB4ALAAAAAAyAEsAAAj9AD0IHEiwoMGDCBMqXFhwmrRpDiNKY0iRYkSIGCE+dPiqokeCGjOKzPjQ1UeLF0eqxCiN0MmEGqmtnLkR1UuDI2VO06mT5jSbNwWmzCiTJ8SeIh8CfZlz51GiT1VKe+XyZEqkRo1KxYjKj9WmWJ06RcoSYtWKV6MWLfpUa1JXXtGCVSuWrdikfypuhHqUrV+MZCWmgmtxb922h6m5TZoq7kKRWf0qHku37M+zCV2pDEvt37/Jdu+yfOXqj2OEQ+v69VyNcmjGXRcaJhuZctTbJf9gPrhSMmK3gae5SkXo9EHDhwH/tT2zq3GDr5ADZr44cElChZ4XfDh7+m/EK/2lpUKlRTtBVJvvhqbWOnhI4qYXEppZWWa11t5FukJlerfBLdJIZ1dYopEkXCqFFJfXQqlIx1dg7k3lnHkFzZdabwUa+Ap/hMTHkB/o0ZfhTK40k6AffoRRUSGucCcifSWNpyCFBuGBSnQv+vRKM4qY5kd5H/kxmEQ5lvXKNIQ01iGNCIGI44VbTbMhKtn5oVtQ4z0JZUgajZegj0F5AGKDQzm4EWmpiKIbkGE6uZeZGEXnZXkLhukBIc1smdJDG1bJpEeoaFbkgQraWVAheqo0nB/+hUmFg4sp1ZgWhhZ0JF87BVdcpQWRCdVaJG1YJ6cehAjZbSxlR+pAFoL3/ZqUolC6qpgYoipNIVTMKlB3i0H0yp83zVWgNKOumt6wv+q6q6uo/gTsS5c2VaCsun6aX5fPnmTqdMG5soWyHkSbHFmxKbvXWoql21Mq1M4KqrrqjpVKFeCOlW6m6MqkSh7gBuJvK9XAq641VlxxiBXgWuOvZwwzPAs0iJSCyCp7IKxsIP+s0vA/K3j2hAwfB1JxNeBWA4gg1mzMMCv+6vFPNSskrHAgKW88Syn+dhGIFSQrW40gpdSsMsuIuEywzIf8E80sG0MzC8v+rtCzrgRbY40sG7fCCtRW0Gwx1f7u0bDV/1hTjTV66GyFNQmbUg0rKnvG8iF6eA3u2hhUszZ22QQLsnbCeP8D98qCBwLIzkcr23XeZte8NcZmA/L1xQrHDQ3LVwByBdvgehDI1qwILfjTNCs8+cWDE771KjsH0nlBLJy8teAssxDz67jn/lFAACH5BAkKAB4ALAAAAAAyAEsAAAj9AD0IHEiwoMGDCBMqXFhwmsOHDl8xnDjxITWHFyFGpMiRoMWL1DKGnJbRYaqOFUmCVMlyZMlpr1ChTIhxZcibOEnqfHhyZkObOIPebBlRpk+BOkEKHRp0Z9GjSZdKFQrxlZ+ZO5VOXVqTpxaUNaVWCzl2KkuTHTFGFVq2LNWRD1F9pbgW51i3N/Ey3flKFN2wdvOSpaZXqdNpqeYuzMpWcGCuGV+lusrw4+PB1e5CPmyVYaq6gcf+++e2sEuehSgnfNU1aOnRbaUmNSl3MejHmU3vjWz1z0LWLcUK1g3XZGrbgB0Pdp3TJkxUf1QjBK61MeGtzhGnOq7ws1rsy/2bni7qZ8tCVFFVLi1trfnKooWiL/wD0SX2zOLfS45eaKEWV2qptxVeZ0WWSiqEaCEdQt4FB557Fh3oxx++MURIgEAJKF5WESGY2oIIVQHgd7fNZhhGkqXyhxZ/EEKRH8AxRtRuIj2nIiHyUaRFgzKmN56BCJY3YUdaoBKjiQWSCNOBOFIIIkN/GKmRcyK9lGIhH7roUyEN1pihWqxth+OQR+FByJEk1ohRKpJBt2J/R3kQJXWzpdlhatFVGKcHfvDoY4BhxucHnHsKJKWSJ14k2ZiFElTId9Wp99AroxBiXqMCUWGRhrstucWTcX5WHVc64YgpQdSN2p5hkoEa/Sd9o77l0IqnDuRHcrIhxl2tW9wG4TTl1ToQrqS+oqewvjYHk6t7smadfYgdWyuxTZHUmbACvRIrV6hcim0znF53GjWTYZvttsqm4q2wzoIXER7megDuSJppBpe68YZ2nb0hpVJFvCrVu29QquQRryCBBMKKwJpZY8UVh1gRrzUJj2axxbNEg0gpiKyyh8TmBvIPKxf/s8JoT8QARQyBfFxNvNVYsYo1JY82CzSBdLEHaStM/E/CNNeMSMKABCLDy+Zas0ogQdfMSikVOwzzz6ORfDErWCccCAtIY+uwNdZYbTHJrCR8BSBSJ631xUFXAzYXeghShTUTC1KN2BdnR1O21mljawXFFlfDNs3VXLGKFf9MjDjTrVgsS9WBnP03yH5X/A/YQWMtCNiFUx4y4DW3sjTRdMfrgcKlzNL0P9DIUjbYgXhuLiCz/BPN2P+0svfDphf0RBerYP2P67H33PvxyHcUEAAh+QQJCgAeACwAAAAAMgBLAAAI/QA9CBxIsKDBgwgTKlxY8BW1h9MewkrFsGLFh9SqPdSI8eErVRZDEuyosVpJkxkhThR5caPJlzBRlnyY6g/LhBhj6ozZ8ZXNmwVd6rS2M+NMaq8KAR0oFKY1olCrEeWJsebSjUalan26VavOqj9FwmoalevTqF5lYixEhaVQqHDNyk3LkabSkDmdSo07d6pMjhPbWiTLV25ZuimpWa2YiuzevWcNI64Li21LvYUj96WKVNWWiq9OTtWsGfJhtTT9MFRF2PTTf7DNdvWLceIfwQkbn3xZ9nVsyTATK/7zWeHYrI8jS/19tmtwiakKhUXY2OXozMnRqtU4TZVlhaz9kW+NC3l22sS2px9MNW33bL7l/aKmpqpm8dxYTR6WzZ8u5Vc1abFQIccNNd5j/8j2UkrcebeFegb94VBT+h1IVILyLchRfX/4AWFBVVS322hencYTR69U9scfAi6USoHuOeeXfFg9xGEh9ym0RXUU7uSfURh9JN2KFVHxYn4++igcNbBw+CBuC+0YEYPiKXlUkzX9IV1IVBQSXk5VznQUdKkYQpwfOTJURSGNtZcflWJ2NJF3KxLJkpYTghknR4A1SecfYagG1B8vRlQXlYiOpYqTdgJFBaHHwQnkoROVueIWgi61IyxTSrokLM6oOORSBO3YEZxxdjZki6QOJP1hXlnFKpEqdbZa0B9vJhmkmWm2auRbRaFUH6a2FsTaiM6hxORixQ5UCLBaJYhaIVU0SxCuMc21IJOj9GorrlmRiJh3UDa7BXImKgvLH9VaO9BYFcJ1XjXMuusBsPIGB4u3xR5rYYUc1esuvPFqJyy/tvobr3Me5WHvu0b1dh59CLeaCmYGa5RKuw8TvHBUKRmSqb0Kb6asKhzbG7G8ClYTC8oPC4RZcsGRAkjMHgSi8z8WmmWFFYg8gbM1gQgC29FHs/JPIKwwHYgVOAdizSqwRQPbCrDFAIXWgXABRTU4VwOIINYgjTQrpnARSIIrDL10ILKY/U80h+hsxdNgl8dczSGllC33P03vbA3UMT9ltDVWIy1LNIEDwkLeD1ujx1OzmL144HcPPnQXgQCSeIKw7XX309aEbUo1Sss9S+A6ax6zFUQfvRxzg7MC+9CwCwJN5Udb3XQXesBO+MOjMwcbK01z9TTOAkm99t+s384808iDfjzyUhM9fNStWA844MhfcTfzBa1QdPWABxJDyuS3735FAQEAIfkECQoAHgAsAAAAADIASwAACP0APQgcSLCgwYMIEypcWBAWLGrUqlGDpUoVw4sXI1bbyHEjRIcWMYocqLGjyY7UVBUamdGkNWvVXsacKbFmqi0sE5aMCVOmT5oeJ/7JaZBjz5dIk/qEyTHlUKICNR5VSvUnR4pPc+5U+s9a169KgU5UhZOlKqNcX4LtGhamRlh/qLCUytOr169rqW60FjFlWYyw0Kq9S/ifYbtJxb4yJBej1LSHI9tli9QktZsYz85MutawZ7CJmUp0WuVi4L1q8eb1PLmy6JSGtLREjbQz67yJPVajmIehIbq1J3+WTNmqRFg3SytU9Xiw6uG4K3fEKnt5Sc6tPxdu29SZoT/K/RP+3oz9Nl7EYXUj35IVYaqaU51vZ1sc6HFVf/4iHE9bPnHQoXVXCHgLpXJafK0lWFxPKDkESH4LAcKcYFUhdhh3NVGU3EJbbFVXgqnVJ9pGsHj3B4QKUfHbdVXRp9eIoxmSSn6NKfTHaUZ9WGGAHsVS0YD6JbQFcx4uVZV9EsWSEpC9MUTFjS6Rx9OUTL02Fn75BSmkKg+dxOCXe6G0myrfndjeQk/8weVOYcIIIzU+VpQKF/mFd1EVhazJZo4wJukMRWWyl9OJE+55knoUqfQHIANCNeSaNR3alETMkfngiVB58CRFEElqmZI//lHIFlqOxF6XkUr6lkoPCpr9qUBbkPKQoSY9FKeZrxKU554MNqhoqVCpCRyY01Xkaq4CxfAehXp59J2dyE5Y4T9ixYIisgMV0hFVlHGkSirQIgtIRGkhRhMsgACb6RYHYpcbadgSVAWz6IkGV7jIBnYUgL2SFW9BzvTHr7dnxqtvuT+lhG+0Ag8m00bf/UuQvjzxK5oqC+eqmbvdSmSIuq9u7HC3TGEs8UBnTbXgxSBnKrKLYSl8skANO7yXj1bM7AE1CK680YM6CxJIILJUjF5MVljBCgs6WwOIINB5xgorgaxCdc4zB/LPKoZFY9gKX1uxghWBXDGvzqs8fRd0VAdiRVcrNG3N0Gt/1jbZVpVUo3M1gqxSt91Da20N1ie/pPU/rQw3NSuCABLIE9bsHchLrdTNyj9UA7JHF4M3Hfjad/HUhRWlWBH5zHPzHfXUgU9OuMSmH05t3Ug9bXrTV8yNuN2YD5105zOTfXhMUlMtk9s6CzS57Nq17fbpOgeyuGqtsP7SKq/PDEjia18+deNWXJF8QSsEIsjUXV3N9Pjstz9SQAAh+QQJCgAeACwAAAAAMgBLAAAI/QA9CBxIsKDBgwgTKlxYcNWqWLEeOgTEsGLFWNWs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El discriminant de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mrow»«/mstyle»«/math» és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«/mrow»«/mstyle»«/math»

]]> 4.04.2.3.6.20 TEORIA: Equacions Biquadrades

Equacions biquadrades

Per resoldre equacions del tipus:
a·(xⁿ)² + b(xⁿ) + c = 0
es fa el canvi de variable t = xⁿ, es troben les solucions de at² + bt + c = 0, i se'n dedueixen les solucions en x.

Exemple:
2x⁴ -20x² + 18 = 0, si t=x², s'escriu: 2t²-20t+18=0.
El discriminant és 256, i les solucions: t = 1 i t = 9.
Com que t és x², les solucions són x = ±1 i y = ±3

]]> 0.0000000 0.0000000 0 4.04.2.3.6.21Q Resol BiquadradaG4 Resol l'equació següent: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

Format de resposta: llista ordenada de menor a major {-3,1,2,4}

]]> 4.04.2.3.6.22Q Resol BiquadradaG4_2 Resol l'equació següent: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

Format de resposta: llista ordenada de menor a major {-3,1,2,4}

]]> 4.04.2.3.6.25Q Resol Biquadrada G6 Resol l'equació següent: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math»

Format de resposta: llista ordenada de menor a major {-3,1,2,4}

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xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>ordena</mi><mo>(</mo><mo>{</mo><mroot><mi>z_1</mi><mn>3</mn></mroot><mo>,</mo><mroot><mi>z_2</mi><mn>3</mn></mroot><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>s1</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow><mrow><mi>s1</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>c</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>s2</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow><mrow><mi>s2</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mfenced close="|" open="|"><mi>b</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mfenced close="|" open="|"><mi>c</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup><mo>-</mo><mn>183</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>24000</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>125</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> D'entrada, es planteja t = x³. L'equació es transforma en:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mrow»«/mstyle»«/math».
Es resol aquesta equació per trobar les dues solucions: t₁ = #z_1 i t₂ = #z_2
Ara cal resoldre x³ = #z_1 i x³ = #z_2

]]> 4.04.2.3.6.30 TEORIA Agrupar E2G

Equació de grau 2 DESORDENADA

Si l'equació està desordenada, cal posar-la en la forma

ax²+ bx + c = 0

Es traslladen, sumant o restant als dos membres, tots els termes a l'esquerra i s'agrupen els de mateix grau. Si hi hz parèntesis o denominadors, es treuen.

Exemple:
3x + 6 =- 10x² + 12x
3x + 6 + 10x² - 12x = 0
10x² - 9x + 6 = 0

]]> 0.0000000 0.0000000 0 4.04.2.3.6.31Q AgruparG2 Parèntesis Transforma a la forma ax² + bx + c = 0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mfenced mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»d«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»f«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«/mrow»«/mstyle»«/math»

Format de la resposta (circumflex pel quadrat): a*x^2+b*x+c=0

]]> 1.0000000 0.5000000 0 0 #r_12 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>*</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>)</mo><mo>-</mo><mi>d</mi><mo>*</mo><mo>(</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>f</mi><mo>)</mo><mo>=</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>*</mo><mo>(</mo><mi>h</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>i</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi><mo>=</mo><mo>(</mo><mi>d</mi><mo>*</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>d</mi><mo>*</mo><mi>f</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_3</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>h</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>g</mi><mo>*</mo><mi>i</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mrow><mi>d</mi><mo>*</mo><mi>e</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_4</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mfenced close="&verbar;" open="&verbar;"><mi>d</mi></mfenced><mo>*</mo><mi>e</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>s_3</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s_3</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>-</mo><mi>g</mi><mo>*</mo><mi>h</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>&Hat;</mo><mn>2</mn><mo>+</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>-</mo><mi>d</mi><mo>*</mo><mi>e</mi><mo>+</mo><mi>g</mi><mo>*</mo><mi>i</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>f</mi><mo>=</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>,</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>i</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>81</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>81</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>105</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>27</mn><mo>=</mo><mo>-</mo><mn>14</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>56</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>58</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>49</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>27</mn><mo>=</mo><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#r_12</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> Primer ens dona:
(#t_1) - (#t_2) = (#t_3);
traient parèntesis:
#t_1 #s_3 #t_4 = #t_3

només cal agrupar a l'esquerra del signe =.

]]> 4.04.2.3.6.32Q AgruparG2 Fracció Transforma a la forma ax² + bx + c = 0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#00007F¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

Format de la resposta (circumflex pel quadrat): a*x^2+b*x+c=0

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mi>a</mi><mo>≠</mo><mi>d</mi></mrow></mfenced></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>d2</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mi>d1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo> </mo><mi>n1</mi><mo>*</mo><mi>d2</mi><mo>-</mo><mi>n2</mi><mo>*</mo><mi>d1</mi><mo>=</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>15</mn><mo>=</mo><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>35</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>31</mn><mo>=</mo><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Si treus denominadors amb el seu mcm, et queda:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]> A partir de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»,

pots multiplicar i escriure: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mrow»«/mstyle»«/math»

i agrupar-ho tot a l'esquerra del signe igual.

]]> 4t ESO/4.04 EQUACIONS/4.04.2 Equació 2n grau/4.04.2.3 E2G3: ax^2+bx+c=0/4.04.2.3.7 Factorizació del 2n grau 4.04.2.3.7.10 TEORIA: FACTORITZACIÓ 2n GRAU

Factorització del 2n grau

Quan l'equació de 2n grau corresponent al polinomi ax² + bx + c té solucions, es pot factoritzar així:

dues(x₁ i x₂):ax² + bx + c = a(x-x₁)(x-x₂)

o una doble (x₁ = x₂): ax² + bx + c = a(x-x₁)²

]]> 0.0000000 0.0000000 0 4.04.2.3.7.11QQ E2G3: Factoritza a(x-x1)(x-x2) Calcula les arrels del polinomi i factoritza:

]]> ]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>s1</mi><mo><</mo><mi>s2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_44</mi><mo>=</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_45</mi><mo>=</mo><mi>s2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>56</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>56</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>484</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>7</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»d«/mi»«/mrow»«/mstyle»«/math»

]]> Les solucions es calculen amb:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/msqrt»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»§#177;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

i ja tens a, x₁ i x₂ per factoritzar.

]]> 4.04.2.3.7.15QQ E2G3: Factoritza a(x-x1)^2 Calcula les arrels del polinomi i factoritza:

]]> ]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>s1</mi><mo><</mo><mi>s2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>s1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>s1</mi><mo>+</mo><mi>s1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>s1</mi><mo>*</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_44</mi><mo>=</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_45</mi><mo>=</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>40</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>40</mn><mo>,</mo><mo>-</mo><mn>200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>10</mn></mrow></mfenced><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfenced mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»d«/mi»«/mstyle»«/math»

]]> La solució doble es calcula amb:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msub mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«msub mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

i ja tens a i x₁ per factoritzar

]]> 4.04.2.3.7.50 TEORIA: FACTORITZACIÓ GRAU SUP A 2

Factorització de polinomis amb grau > 2

Si tenim un polinomi de grau superior a 2 sense terme independent, alguns cops es pot treure x en factor per fer aparèixer una equació de 2n grau.

Per exemple:

x³ - 5x² + 6x = 0 s'escriu x(x² - 5x + 6) = 0

En aquest cas, i com que x² - 5x+ 6 té per solucions 2 i 3, la factorització del polinomi és: x (x-2)(x-3)

Si el polinomi té terme independent, es pot factoritzar amb el mètode de Ruffini (a 1r de btx!)

]]> 0.0000000 0.0000000 0 4t ESO/4.04 EQUACIONS/4.04.2 Equació 2n grau/4.04.2.4 Problemes EG2 4.04.2.4.11Q Nombre enter solució

Trobeu un nombre enter, no nul, tal que el doble de seu quadrat sigui #b vegades aquest nombre.

]]> 1.0000000 0.5000000 0 0 #a <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#a</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> L'equació s'escriu 2x² = #b x, o sigui 2x² - #b x = 0.
Es resol traient x en factor (que dona la solució nul·la) i (2x - #b) que dona l'altra solució

]]> 4.04.2.4.12Q QuadratNombresNaturalsConsecutius

La suma dels quadrats de dos nombres naturals consecutius és #b.

a) Quin és el més petit?

b) Quin és el més gran?

]]> 1.0000000 0.5000000 0 0 a) =#ab) =#d]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>a</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>b</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>-</mo><mi>b</mi><mo>=</mo><mn>0</mn></mrow></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">d</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> L'equació s'escriu x² + (x+1)² = #b, o sigui 2x² +2x +1 = #b.
Cal doncs resoldre: 2x² +2x - #e = 0.
Com que són naturals, la resposta ha de ser positiva.

]]> 4.04.2.4.13QNombresNaturalsMultiplicatsDDQ

Trobeu dos nombres naturals, que multiplicats donin #s i tal que, la diferència dels seus quadrats sigui #d.

a) Quin és el més petit?

b) Quin és el més gran?

]]> 1.0000000 0.2500000 0 0 a) =#ab) =#d]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mfrac><msup><mi>s</mi><mn>2</mn></msup><msup><mi>x</mi><mn>2</mn></msup></mfrac><mo>=</mo><mi>d</mi></mrow></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a</mi><mo><</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><msup><mi>s</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><msup><mi>d</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mo>-</mo><msqrt><mi>D</mi></msqrt></mrow><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mo>+</mo><msqrt><mi>D</mi></msqrt></mrow><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1681</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>,</mo><mi>t2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>,</mo><mo>-</mo><mn>16</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">d</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Si x és el més gran y el més petit, i el producte xy = #s, aleshores «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»s«/mi»«/mrow»«mi mathvariant=¨bold¨»x«/mi»«/mfrac»«/mrow»«/mstyle»«/math»

La diferència de quadrats és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»s«/mi»«/mrow»«mi mathvariant=¨bold¨»x«/mi»«/mfrac»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«/mrow»«/mstyle»«/math»

Eleva la fracció al quadrat, treu el denominador i tens una equació biquadrada: x⁴ - #d x² - #s1 = 0

]]> L'equació biquadrada si t = x² s'escriu: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

El seu discriminant és #D i les seves solucions #t1 i #t2.

Com t =x², la solució negativa (#t1) no serveix.

]]> Com t =x², la solució negativa (#t1) no serveix.

I per tant, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msqrt mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«/mrow»«/mstyle»«/math»

]]> 4.04.2.4.21Q Edat

D'aquí a #a1 el quadrat més el doble de la meva edat serà igual a #a2.

Quants anys tinc?

]]> 1.0000000 0.5000000 0 0 #s1 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><msup><mi>s1</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>=</mo><mi>a2</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>48</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>8</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>6</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#s1</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> L'equació s'escriu «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8660;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mstyle»«/math» i té dues solucions
Només és vàlida la solució positiva!

]]> 4.04.2.4.31Q Geometria rectangle

Un camp rectangular té una superfície de #s m² i #y m més de llarg que d'ample.
Calculeu les dimensions del camp.

]]> 1.0000000 0.5000000 0 0 llarg=#aample=#b]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>199</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>y</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>s</mi><mo>=</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>44884</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>229</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>196</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>,</mo><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>229</mn><mo>,</mo><mn>196</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>229</mn><mo>,</mo><mn>196</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi>g</mi><mo>=</mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>b</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> L'equació s'escriu (x + #y)· x = #s, o sigui x² + #y x - #s = 0. Només ens valen els valors positius.

]]> 4.04.2.4.32Q GeometriaRectangleTriangle

El quadrat té per costat x.
El triangle té per altura x i per base #b.

Quin és el valor de x si l'àrea de la figura és #a.

]]> 4.04.2.4.33Q GeometriaPitàgores

En un triangle rectangle, el catet b mesura x+#b i el catet c mesura x+#c.

Si la hipotenusa a del triangle mesura #a,quin és el valor de x?

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»c«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8660;«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8660;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math»

i només la solució positiva és acceptable!

]]> 4.04.2.4.34Q GeometriaPitàgoresPerímetre

D'un triangle rectangle sabem la hipotenusa, #a1, i el perímetre, #P.

Determina quant mesuren els catets b i c si b és més gran que c.

]]> 1.0000000 0.3333333 0 0 b=#b1c=#c1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>99</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>99</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><msqrt><mrow><msup><mi>b1</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c1</mi><mn>2</mn></msup></mrow></msqrt></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>b1</mi><mo>></mo><mi>c1</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a1</mi><mo>∈</mo><naturalnumbers/></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>b1</mi><mo>+</mo><mi>c1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>P</mi><mo>-</mo><mi>a1</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mfenced><mi>e1</mi></mfenced><mn>2</mn></msup><mo>-</mo><msup><mi>a1</mi><mn>2</mn></msup><mo>=</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>,</mo><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>89</mn><mo>,</mo><mn>80</mn><mo>,</mo><mn>39</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>208</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>b</mi><mo>+</mo><mn>119</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>#</mo><mi>b</mi><mn>1</mn><mspace linebreak="newline"/><mi>c</mi><mo>=</mo><mo>#</mo><mi>c</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Del perímetre, es dedueix que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«/mstyle»«/math».

Ara, aplica el teorema de Pitàgores

]]> Aplicant el teorema de Pitàgores:

ja tens l'equació en b. Només pots fer servir la solució positiva per b. Per a calcular c, fes servir «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mrow»«/mstyle»«/math»

]]> 4.04.2.4.41Q Graf

Representació de la situació amb 4 torres

En un parc nacional, hi han torres de vigilància. De cada torre surten camins cap a les altres torres.

Si en total, hi ha #c camins, quantes torres hi ha?

]]> Amb intuïció es pot fer sense càlculs!

Quantes torres hi ha en total? Pots escriure l'equació?

]]> Si de cada torre surten (x-1) camins, el nombre total de camins és x·(x-1).

L'equació és:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8660;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mstyle»«/math»

Només pots fer servir la solució positiva

]]> 4t ESO/4.04 EQUACIONS/4.04.2 Equació 2n grau/4.04.2.5 Aplicacions E2G 4.04.2.5.10 Energia total

Conservació de l'energia mecànica

Exemple de conservació d'energia en xocs elàstics

«Newtons cradle animation book» de DemonDeLuxe (Dominique Toussaint) CC

L'energia mecànica d'un cos de massa m, que es mou a velocitat v i situat a una altura h es calcula amb:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»E«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»mv«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»mgh«/mi»«/mrow»«/mstyle»«/math»

Unitats: E(joules), m(kg), v(m/s), g=9,8 m/s² i h(m)

En un sistema aïllat, l'energia mecànica es manté constant; els canvis de velocitat van acompanyats de canvis d'altura i viceversa.

L'energia cinètica és E_C = 1/2 mv2

i l'energia potencial E_P = mgh

]]> 0.0000000 0.0000000 0 4.04.2.5.11Q EnergiaMecànica

Si la poma pesa #m1 g i cau des d'una altura de #h1 m, amb quina velocitat (positiva) impacta en el cap?

Feu servir el valor aproximat per g = 9,8 m/s²

Format: velocitat arrodonida als centèsims

En el moment de l'impacte, ja no hi ha altura i l'energia potencial és nul·la; en canvi l'energia cinètica és mv²/2.

Com que l'energia es conserva, l'energia cinètica final és igual a l'energia potencial inicial:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»mv«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»mgh«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8660;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»gh«/mi»«/mrow»«/mstyle»«/math»

Ja pots calcular v.

FIXA'T QUE LA VELOCITAT NO DEPÈN DE LA MASSA

]]> 4.04.2.5.20 MRUA

MRUA

En aquest moviment la trajectòria és una recta i l'acceleració és constant.

Les equacions d'aquest moviment són (si el temps a l'inici és 0):

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Unitats: v i v₀ (velocitat) en m/s, a (acceleració) en m/s², t (temps) en segons, x (desplaçament) i x₀ (desplaçament a l'instant t = 0) en m

]]> 0.0000000 0.0000000 0 4.04.2.5.21Q MRUA

En una carretera rectilínia, arriba un cotxe amb una velocitat de #v1 m/s a l'instant 0. Si la seva acceleració és constant i és de #a1 m/s², quant trigarà a recórrer #x1 km?

Format: segons arrodonits a la unitat

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