L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(\left(8-11\right)\times\dfrac{66}{7}+8+8+\dfrac{121}{8}+\dfrac{\dfrac{\dfrac{33}{10}}{\dfrac{59}{7}}}{-2}+\dfrac{\dfrac{-2}{-7}}{8}\right)\times\left(-\dfrac{142}{5}\right)\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(\left(8-11\right)\times\dfrac{66}{7}+8+8+\dfrac{121}{8}+\dfrac{\dfrac{\dfrac{33}{10}}{\dfrac{59}{7}}}{-2}+\dfrac{\dfrac{-2}{-7}}{8}\right)\times\left(-\dfrac{142}{5}\right)=-\dfrac{448933}{5900}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(\left(8-11\right)\times\dfrac{66}{7}+8+8+\dfrac{121}{8}+\dfrac{\dfrac{231}{590}}{-2}+\dfrac{\dfrac{-2}{-7}}{8}\right)\times\left(-\dfrac{142}{5}\right)\\&=&\left(\left(8-11\right)\times\dfrac{66}{7}+8+8+\dfrac{121}{8}-\dfrac{231}{1180}+\dfrac{\dfrac{-2}{-7}}{8}\right)\times\left(-\dfrac{142}{5}\right)\\&=&\left(\left(8-11\right)\times\dfrac{66}{7}+8+8+\dfrac{121}{8}-\dfrac{231}{1180}+\dfrac{\dfrac{2}{7}}{8}\right)\times\left(-\dfrac{142}{5}\right)\\&=&\left(\left(8-11\right)\times\dfrac{66}{7}+8+8+\dfrac{121}{8}-\dfrac{231}{1180}+\dfrac{1}{28}\right)\times\left(-\dfrac{142}{5}\right)\\&=&\left(-3\times\dfrac{66}{7}+8+8+\dfrac{121}{8}-\dfrac{231}{1180}+\dfrac{1}{28}\right)\times\left(-\dfrac{142}{5}\right)\\&=&\left(-3\times\dfrac{66}{7}+8+\dfrac{185}{8}-\dfrac{231}{1180}+\dfrac{1}{28}\right)\times\left(-\dfrac{142}{5}\right)\\&=&\left(-3\times\dfrac{66}{7}+8+\dfrac{185}{8}-\dfrac{661}{4130}\right)\times\left(-\dfrac{142}{5}\right)\\&=&\left(-\dfrac{198}{7}+8+\dfrac{185}{8}-\dfrac{661}{4130}\right)\times\left(-\dfrac{142}{5}\right)\\&=&\left(-\dfrac{198}{7}+8+\dfrac{379381}{16520}\right)\times\left(-\dfrac{142}{5}\right)\\&=&\left(-\dfrac{142}{7}+\dfrac{379381}{16520}\right)\times\left(-\dfrac{142}{5}\right)\\&=&\dfrac{6323}{2360}\times\left(-\dfrac{142}{5}\right)\\&=&-\dfrac{448933}{5900}\\
\end{eqnarray*}