L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(\dfrac{8}{5}-\left(\dfrac{-\dfrac{79}{7}}{11}+\dfrac{8}{7}\times\left(-\dfrac{133}{3}\right)\times\left(-\dfrac{99}{2}\right)+\dfrac{-\dfrac{91}{10}}{11}\right)\times6\times\dfrac{\dfrac{-\dfrac{79}{7}}{\dfrac{8}{5}}}{\dfrac{8}{7}+\dfrac{133}{3}}-3\right)\times12\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(\dfrac{8}{5}-\left(\dfrac{-\dfrac{79}{7}}{11}+\dfrac{8}{7}\times\left(-\dfrac{133}{3}\right)\times\left(-\dfrac{99}{2}\right)+\dfrac{-\dfrac{91}{10}}{11}\right)\times6\times\dfrac{\dfrac{-\dfrac{79}{7}}{\dfrac{8}{5}}}{\dfrac{8}{7}+\dfrac{133}{3}}-3\right)\times12=\dfrac{82272994260}{2941400}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(\dfrac{8}{5}-\left(-\dfrac{79}{77}+\dfrac{8}{7}\times\left(-\dfrac{133}{3}\right)\times\left(-\dfrac{99}{2}\right)+\dfrac{-\dfrac{91}{10}}{11}\right)\times6\times\dfrac{\dfrac{-\dfrac{79}{7}}{\dfrac{8}{5}}}{\dfrac{8}{7}+\dfrac{133}{3}}-3\right)\times12\\&=&\left(\dfrac{8}{5}-\left(-\dfrac{79}{77}+\left(-\dfrac{152}{3}\right)\times\left(-\dfrac{99}{2}\right)+\dfrac{-\dfrac{91}{10}}{11}\right)\times6\times\dfrac{\dfrac{-\dfrac{79}{7}}{\dfrac{8}{5}}}{\dfrac{8}{7}+\dfrac{133}{3}}-3\right)\times12\\&=&\left(\dfrac{8}{5}-\left(-\dfrac{79}{77}+2508+\dfrac{-\dfrac{91}{10}}{11}\right)\times6\times\dfrac{\dfrac{-\dfrac{79}{7}}{\dfrac{8}{5}}}{\dfrac{8}{7}+\dfrac{133}{3}}-3\right)\times12\\&=&\left(\dfrac{8}{5}-\left(-\dfrac{79}{77}+2508-\dfrac{91}{110}\right)\times6\times\dfrac{\dfrac{-\dfrac{79}{7}}{\dfrac{8}{5}}}{\dfrac{8}{7}+\dfrac{133}{3}}-3\right)\times12\\&=&\left(\dfrac{8}{5}-\left(-\dfrac{79}{77}+2508-\dfrac{91}{110}\right)\times6\times\dfrac{\dfrac{-\dfrac{79}{7}}{\dfrac{8}{5}}}{\dfrac{955}{21}}-3\right)\times12\\&=&\left(\dfrac{8}{5}-\left(\dfrac{193037}{77}-\dfrac{91}{110}\right)\times6\times\dfrac{\dfrac{-\dfrac{79}{7}}{\dfrac{8}{5}}}{\dfrac{955}{21}}-3\right)\times12\\&=&\left(\dfrac{8}{5}-\dfrac{1929733}{770}\times6\times\dfrac{\dfrac{-\dfrac{79}{7}}{\dfrac{8}{5}}}{\dfrac{955}{21}}-3\right)\times12\\&=&\left(\dfrac{8}{5}-\dfrac{1929733}{770}\times6\times\dfrac{-\dfrac{395}{56}}{\dfrac{955}{21}}-3\right)\times12\\&=&\left(\dfrac{8}{5}-\dfrac{1929733}{770}\times6\times\left(-\dfrac{237}{1528}\right)-3\right)\times12\\&=&\left(\dfrac{8}{5}-\dfrac{5789199}{385}\times\left(-\dfrac{237}{1528}\right)-3\right)\times12\\&=&\left(\dfrac{8}{5}+\dfrac{1372040163}{588280}-3\right)\times12\\&=&\left(\dfrac{6864907055}{2941400}-3\right)\times12\\&=&\dfrac{6856082855}{2941400}\times12\\&=&\dfrac{82272994260}{2941400}\\
\end{eqnarray*}