L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(-4\right)\times\left(-2+\dfrac{59}{5}\right)\times\left(\dfrac{\dfrac{\left(-2\right)\times\left(-7\right)\times\dfrac{8}{-\dfrac{115}{4}}}{\dfrac{-\dfrac{47}{6}}{-\dfrac{76}{5}}-12-3+\left(-4\right)\times\left(-\dfrac{59}{5}\right)\times\left(-3\right)}}{-7}+\dfrac{47}{6}\right)\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(-4\right)\times\left(-2+\dfrac{59}{5}\right)\times\left(\dfrac{\dfrac{\left(-2\right)\times\left(-7\right)\times\dfrac{8}{-\dfrac{115}{4}}}{\dfrac{-\dfrac{47}{6}}{-\dfrac{76}{5}}-12-3+\left(-4\right)\times\left(-\dfrac{59}{5}\right)\times\left(-3\right)}}{-7}+\dfrac{47}{6}\right)=-\dfrac{75366627364}{245552370}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-4\right)\times\left(-2+\dfrac{59}{5}\right)\times\left(\dfrac{\dfrac{\left(-2\right)\times\left(-7\right)\times\left(-\dfrac{32}{115}\right)}{\dfrac{-\dfrac{47}{6}}{-\dfrac{76}{5}}-12-3+\left(-4\right)\times\left(-\dfrac{59}{5}\right)\times\left(-3\right)}}{-7}+\dfrac{47}{6}\right)\\&=&\left(-4\right)\times\left(-2+\dfrac{59}{5}\right)\times\left(\dfrac{\dfrac{\left(-2\right)\times\left(-7\right)\times\left(-\dfrac{32}{115}\right)}{\dfrac{235}{456}-12-3+\left(-4\right)\times\left(-\dfrac{59}{5}\right)\times\left(-3\right)}}{-7}+\dfrac{47}{6}\right)\\&=&\left(-4\right)\times\left(-2+\dfrac{59}{5}\right)\times\left(\dfrac{\dfrac{\left(-2\right)\times\left(-7\right)\times\left(-\dfrac{32}{115}\right)}{\dfrac{235}{456}-12-3+\dfrac{236}{5}\times\left(-3\right)}}{-7}+\dfrac{47}{6}\right)\\&=&\left(-4\right)\times\left(-2+\dfrac{59}{5}\right)\times\left(\dfrac{\dfrac{\left(-2\right)\times\left(-7\right)\times\left(-\dfrac{32}{115}\right)}{\dfrac{235}{456}-12-3-\dfrac{708}{5}}}{-7}+\dfrac{47}{6}\right)\\&=&\left(-4\right)\times\left(-2+\dfrac{59}{5}\right)\times\left(\dfrac{\dfrac{14\times\left(-\dfrac{32}{115}\right)}{\dfrac{235}{456}-12-3-\dfrac{708}{5}}}{-7}+\dfrac{47}{6}\right)\\&=&\left(-4\right)\times\left(-2+\dfrac{59}{5}\right)\times\left(\dfrac{\dfrac{-\dfrac{448}{115}}{\dfrac{235}{456}-12-3-\dfrac{708}{5}}}{-7}+\dfrac{47}{6}\right)\\&=&\left(-4\right)\times\left(-2+\dfrac{59}{5}\right)\times\left(\dfrac{\dfrac{-\dfrac{448}{115}}{-\dfrac{5237}{456}-3-\dfrac{708}{5}}}{-7}+\dfrac{47}{6}\right)\\&=&\left(-4\right)\times\left(-2+\dfrac{59}{5}\right)\times\left(\dfrac{\dfrac{-\dfrac{448}{115}}{-\dfrac{6605}{456}-\dfrac{708}{5}}}{-7}+\dfrac{47}{6}\right)\\&=&\left(-4\right)\times\left(-2+\dfrac{59}{5}\right)\times\left(\dfrac{\dfrac{-\dfrac{448}{115}}{-\dfrac{355873}{2280}}}{-7}+\dfrac{47}{6}\right)\\&=&\left(-4\right)\times\left(-2+\dfrac{59}{5}\right)\times\left(\dfrac{\dfrac{29184}{1169297}}{-7}+\dfrac{47}{6}\right)\\&=&\left(-4\right)\times\left(-2+\dfrac{59}{5}\right)\times\left(-\dfrac{29184}{8185079}+\dfrac{47}{6}\right)\\&=&\left(-4\right)\times\dfrac{49}{5}\times\left(-\dfrac{29184}{8185079}+\dfrac{47}{6}\right)\\&=&\left(-4\right)\times\dfrac{49}{5}\times\dfrac{384523609}{49110474}\\&=&\left(-\dfrac{196}{5}\right)\times\dfrac{384523609}{49110474}\\&=&-\dfrac{75366627364}{245552370}\\
\end{eqnarray*}