L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(-\dfrac{123}{4}-\dfrac{\dfrac{-7}{-\dfrac{123}{4}}}{-\dfrac{94}{5}}-1-\left(-\dfrac{94}{5}\right)\times\left(-5\right)\times\dfrac{8}{3}\times\dfrac{\dfrac{\dfrac{\dfrac{49}{4}}{-6}}{\dfrac{8}{3}}}{\dfrac{\dfrac{-11}{5}}{-\dfrac{123}{4}}}\times\left(-1\right)\right)+10\]
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Exercice
On a \( X=\left(-\dfrac{123}{4}-\dfrac{\dfrac{-7}{-\dfrac{123}{4}}}{-\dfrac{94}{5}}-1-\left(-\dfrac{94}{5}\right)\times\left(-5\right)\times\dfrac{8}{3}\times\dfrac{\dfrac{\dfrac{\dfrac{49}{4}}{-6}}{\dfrac{8}{3}}}{\dfrac{\dfrac{-11}{5}}{-\dfrac{123}{4}}}\times\left(-1\right)\right)+10=-\dfrac{11005656652}{4069824}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-\dfrac{123}{4}-\dfrac{\dfrac{-7}{-\dfrac{123}{4}}}{-\dfrac{94}{5}}-1-\left(-\dfrac{94}{5}\right)\times\left(-5\right)\times\dfrac{8}{3}\times\dfrac{\dfrac{\dfrac{\dfrac{49}{4}}{-6}}{\dfrac{8}{3}}}{\dfrac{-\dfrac{11}{5}}{-\dfrac{123}{4}}}\times\left(-1\right)\right)+10\\&=&\left(-\dfrac{123}{4}-\dfrac{\dfrac{-7}{-\dfrac{123}{4}}}{-\dfrac{94}{5}}-1-\left(-\dfrac{94}{5}\right)\times\left(-5\right)\times\dfrac{8}{3}\times\dfrac{\dfrac{\dfrac{\dfrac{49}{4}}{-6}}{\dfrac{8}{3}}}{\dfrac{44}{615}}\times\left(-1\right)\right)+10\\&=&\left(-\dfrac{123}{4}-\dfrac{\dfrac{-7}{-\dfrac{123}{4}}}{-\dfrac{94}{5}}-1-94\times\dfrac{8}{3}\times\dfrac{\dfrac{\dfrac{\dfrac{49}{4}}{-6}}{\dfrac{8}{3}}}{\dfrac{44}{615}}\times\left(-1\right)\right)+10\\&=&\left(-\dfrac{123}{4}-\dfrac{\dfrac{-7}{-\dfrac{123}{4}}}{-\dfrac{94}{5}}-1-\dfrac{752}{3}\times\dfrac{\dfrac{\dfrac{\dfrac{49}{4}}{-6}}{\dfrac{8}{3}}}{\dfrac{44}{615}}\times\left(-1\right)\right)+10\\&=&\left(-\dfrac{123}{4}-\dfrac{\dfrac{-7}{-\dfrac{123}{4}}}{-\dfrac{94}{5}}-1-\dfrac{752}{3}\times\dfrac{\dfrac{-\dfrac{49}{24}}{\dfrac{8}{3}}}{\dfrac{44}{615}}\times\left(-1\right)\right)+10\\&=&\left(-\dfrac{123}{4}-\dfrac{\dfrac{-7}{-\dfrac{123}{4}}}{-\dfrac{94}{5}}-1-\dfrac{752}{3}\times\dfrac{-\dfrac{49}{64}}{\dfrac{44}{615}}\times\left(-1\right)\right)+10\\&=&\left(-\dfrac{123}{4}-\dfrac{\dfrac{-7}{-\dfrac{123}{4}}}{-\dfrac{94}{5}}-1-\dfrac{752}{3}\times\left(-\dfrac{30135}{2816}\right)\times\left(-1\right)\right)+10\\&=&\left(-\dfrac{123}{4}-\dfrac{\dfrac{28}{123}}{-\dfrac{94}{5}}-1-\dfrac{752}{3}\times\left(-\dfrac{30135}{2816}\right)\times\left(-1\right)\right)+10\\&=&\left(-\dfrac{123}{4}+\dfrac{70}{5781}-1-\dfrac{752}{3}\times\left(-\dfrac{30135}{2816}\right)\times\left(-1\right)\right)+10\\&=&\left(-\dfrac{123}{4}+\dfrac{70}{5781}-1-\left(-\dfrac{472115}{176}\right)\times\left(-1\right)\right)+10\\&=&\left(-\dfrac{123}{4}+\dfrac{70}{5781}-1-\dfrac{472115}{176}\right)+10\\&=&\left(-\dfrac{710783}{23124}-1-\dfrac{472115}{176}\right)+10\\&=&\left(-\dfrac{733907}{23124}-\dfrac{472115}{176}\right)+10\\&=&-\dfrac{11046354892}{4069824}+10\\&=&-\dfrac{11005656652}{4069824}\\
\end{eqnarray*}