L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{102}{11}+\dfrac{\left(-\dfrac{49}{6}\right)\times\left(-11-\left(-\dfrac{76}{11}\right)\times\left(-\dfrac{39}{2}\right)-\dfrac{\dfrac{10}{3}}{-\dfrac{49}{6}}\right)}{-4}+\left(-\dfrac{39}{2}\right)\times\dfrac{\dfrac{-\dfrac{39}{2}}{5}}{\dfrac{55}{8}+\dfrac{79}{2}+11-\dfrac{79}{2}+5}\]
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Exercice
On a \( X=\dfrac{102}{11}+\dfrac{\left(-\dfrac{49}{6}\right)\times\left(-11-\left(-\dfrac{76}{11}\right)\times\left(-\dfrac{39}{2}\right)-\dfrac{\dfrac{10}{3}}{-\dfrac{49}{6}}\right)}{-4}+\left(-\dfrac{39}{2}\right)\times\dfrac{\dfrac{-\dfrac{39}{2}}{5}}{\dfrac{55}{8}+\dfrac{79}{2}+11-\dfrac{79}{2}+5}=-\dfrac{7625133}{26840}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{102}{11}+\dfrac{\left(-\dfrac{49}{6}\right)\times\left(-11-\dfrac{1482}{11}-\dfrac{\dfrac{10}{3}}{-\dfrac{49}{6}}\right)}{-4}+\left(-\dfrac{39}{2}\right)\times\dfrac{\dfrac{-\dfrac{39}{2}}{5}}{\dfrac{55}{8}+\dfrac{79}{2}+11-\dfrac{79}{2}+5}\\&=&\dfrac{102}{11}+\dfrac{\left(-\dfrac{49}{6}\right)\times\left(-11-\dfrac{1482}{11}+\dfrac{20}{49}\right)}{-4}+\left(-\dfrac{39}{2}\right)\times\dfrac{\dfrac{-\dfrac{39}{2}}{5}}{\dfrac{55}{8}+\dfrac{79}{2}+11-\dfrac{79}{2}+5}\\&=&\dfrac{102}{11}+\dfrac{\left(-\dfrac{49}{6}\right)\times\left(-11-\dfrac{1482}{11}+\dfrac{20}{49}\right)}{-4}+\left(-\dfrac{39}{2}\right)\times\dfrac{\dfrac{-\dfrac{39}{2}}{5}}{\dfrac{55}{8}+\dfrac{101}{2}-\dfrac{79}{2}+5}\\&=&\dfrac{102}{11}+\dfrac{\left(-\dfrac{49}{6}\right)\times\left(-11-\dfrac{1482}{11}+\dfrac{20}{49}\right)}{-4}+\left(-\dfrac{39}{2}\right)\times\dfrac{\dfrac{-\dfrac{39}{2}}{5}}{\dfrac{55}{8}+11+5}\\&=&\dfrac{102}{11}+\dfrac{\left(-\dfrac{49}{6}\right)\times\left(-\dfrac{1603}{11}+\dfrac{20}{49}\right)}{-4}+\left(-\dfrac{39}{2}\right)\times\dfrac{\dfrac{-\dfrac{39}{2}}{5}}{\dfrac{55}{8}+11+5}\\&=&\dfrac{102}{11}+\dfrac{\left(-\dfrac{49}{6}\right)\times-\dfrac{78327}{539}}{-4}+\left(-\dfrac{39}{2}\right)\times\dfrac{\dfrac{-\dfrac{39}{2}}{5}}{\dfrac{55}{8}+11+5}\\&=&\dfrac{102}{11}+\dfrac{\left(-\dfrac{49}{6}\right)\times-\dfrac{78327}{539}}{-4}+\left(-\dfrac{39}{2}\right)\times\dfrac{\dfrac{-\dfrac{39}{2}}{5}}{\dfrac{143}{8}+5}\\&=&\dfrac{102}{11}+\dfrac{\left(-\dfrac{49}{6}\right)\times-\dfrac{78327}{539}}{-4}+\left(-\dfrac{39}{2}\right)\times\dfrac{\dfrac{-\dfrac{39}{2}}{5}}{\dfrac{183}{8}}\\&=&\dfrac{102}{11}+\dfrac{\dfrac{26109}{22}}{-4}+\left(-\dfrac{39}{2}\right)\times\dfrac{\dfrac{-\dfrac{39}{2}}{5}}{\dfrac{183}{8}}\\&=&\dfrac{102}{11}+\dfrac{\dfrac{26109}{22}}{-4}+\left(-\dfrac{39}{2}\right)\times\dfrac{-\dfrac{39}{10}}{\dfrac{183}{8}}\\&=&\dfrac{102}{11}+\dfrac{\dfrac{26109}{22}}{-4}+\left(-\dfrac{39}{2}\right)\times\left(-\dfrac{52}{305}\right)\\&=&\dfrac{102}{11}-\dfrac{26109}{88}+\left(-\dfrac{39}{2}\right)\times\left(-\dfrac{52}{305}\right)\\&=&\dfrac{102}{11}-\dfrac{26109}{88}+\dfrac{1014}{305}\\&=&-\dfrac{25293}{88}+\dfrac{1014}{305}\\&=&-\dfrac{7625133}{26840}\\
\end{eqnarray*}