L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
Si vous regénérez la page (F5) les valeurs seront changées.
La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{\dfrac{\dfrac{117}{8}}{-\dfrac{123}{7}}}{-\dfrac{62}{3}}-8+7\times\dfrac{\dfrac{\left(-2\right)\times11\times\left(-\dfrac{62}{3}\right)-8-\dfrac{37}{2}}{\dfrac{\dfrac{-\dfrac{123}{7}}{-3}}{-\dfrac{25}{3}}-\left(-\dfrac{123}{7}\right)\times7}}{-2}\times\left(-2\right)\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{117}{8}}{-\dfrac{123}{7}}}{-\dfrac{62}{3}}-8+7\times\dfrac{\dfrac{\left(-2\right)\times11\times\left(-\dfrac{62}{3}\right)-8-\dfrac{37}{2}}{\dfrac{\dfrac{-\dfrac{123}{7}}{-3}}{-\dfrac{25}{3}}-\left(-\dfrac{123}{7}\right)\times7}}{-2}\times\left(-2\right)=\dfrac{43211978372}{2611386432}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{117}{8}}{-\dfrac{123}{7}}}{-\dfrac{62}{3}}-8+7\times\dfrac{\dfrac{\left(-22\right)\times\left(-\dfrac{62}{3}\right)-8-\dfrac{37}{2}}{\dfrac{\dfrac{-\dfrac{123}{7}}{-3}}{-\dfrac{25}{3}}-\left(-\dfrac{123}{7}\right)\times7}}{-2}\times\left(-2\right)\\&=&\dfrac{\dfrac{\dfrac{117}{8}}{-\dfrac{123}{7}}}{-\dfrac{62}{3}}-8+7\times\dfrac{\dfrac{\dfrac{1364}{3}-8-\dfrac{37}{2}}{\dfrac{\dfrac{-\dfrac{123}{7}}{-3}}{-\dfrac{25}{3}}-\left(-\dfrac{123}{7}\right)\times7}}{-2}\times\left(-2\right)\\&=&\dfrac{\dfrac{\dfrac{117}{8}}{-\dfrac{123}{7}}}{-\dfrac{62}{3}}-8+7\times\dfrac{\dfrac{\dfrac{1364}{3}-8-\dfrac{37}{2}}{\dfrac{\dfrac{41}{7}}{-\dfrac{25}{3}}-\left(-\dfrac{123}{7}\right)\times7}}{-2}\times\left(-2\right)\\&=&\dfrac{\dfrac{\dfrac{117}{8}}{-\dfrac{123}{7}}}{-\dfrac{62}{3}}-8+7\times\dfrac{\dfrac{\dfrac{1364}{3}-8-\dfrac{37}{2}}{-\dfrac{123}{175}-\left(-\dfrac{123}{7}\right)\times7}}{-2}\times\left(-2\right)\\&=&\dfrac{\dfrac{\dfrac{117}{8}}{-\dfrac{123}{7}}}{-\dfrac{62}{3}}-8+7\times\dfrac{\dfrac{\dfrac{1364}{3}-8-\dfrac{37}{2}}{-\dfrac{123}{175}+123}}{-2}\times\left(-2\right)\\&=&\dfrac{\dfrac{\dfrac{117}{8}}{-\dfrac{123}{7}}}{-\dfrac{62}{3}}-8+7\times\dfrac{\dfrac{\dfrac{1340}{3}-\dfrac{37}{2}}{-\dfrac{123}{175}+123}}{-2}\times\left(-2\right)\\&=&\dfrac{\dfrac{\dfrac{117}{8}}{-\dfrac{123}{7}}}{-\dfrac{62}{3}}-8+7\times\dfrac{\dfrac{\dfrac{2569}{6}}{-\dfrac{123}{175}+123}}{-2}\times\left(-2\right)\\&=&\dfrac{\dfrac{\dfrac{117}{8}}{-\dfrac{123}{7}}}{-\dfrac{62}{3}}-8+7\times\dfrac{\dfrac{\dfrac{2569}{6}}{\dfrac{21402}{175}}}{-2}\times\left(-2\right)\\&=&\dfrac{\dfrac{\dfrac{117}{8}}{-\dfrac{123}{7}}}{-\dfrac{62}{3}}-8+7\times\dfrac{\dfrac{449575}{128412}}{-2}\times\left(-2\right)\\&=&\dfrac{\dfrac{\dfrac{117}{8}}{-\dfrac{123}{7}}}{-\dfrac{62}{3}}-8+7\times\left(-\dfrac{449575}{256824}\right)\times\left(-2\right)\\&=&\dfrac{-\dfrac{273}{328}}{-\dfrac{62}{3}}-8+7\times\left(-\dfrac{449575}{256824}\right)\times\left(-2\right)\\&=&\dfrac{819}{20336}-8+7\times\left(-\dfrac{449575}{256824}\right)\times\left(-2\right)\\&=&\dfrac{819}{20336}-8+\left(-\dfrac{3147025}{256824}\right)\times\left(-2\right)\\&=&\dfrac{819}{20336}-8+\dfrac{3147025}{128412}\\&=&-\dfrac{161869}{20336}+\dfrac{3147025}{128412}\\&=&\dfrac{43211978372}{2611386432}\\
\end{eqnarray*}