L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{\dfrac{\dfrac{\dfrac{10}{11}}{\dfrac{115}{2}}+11}{-5-\dfrac{20}{11}-11}}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{104}{9}}}{-\dfrac{104}{9}}}{\dfrac{\dfrac{-\dfrac{104}{9}}{-\dfrac{104}{9}+\dfrac{104}{9}-\dfrac{143}{3}\times\dfrac{143}{3}\times\dfrac{143}{3}\times\left(-\dfrac{104}{9}\right)}}{\dfrac{10}{11}}}}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{\dfrac{10}{11}}{\dfrac{115}{2}}+11}{-5-\dfrac{20}{11}-11}}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{104}{9}}}{-\dfrac{104}{9}}}{\dfrac{\dfrac{-\dfrac{104}{9}}{-\dfrac{104}{9}+\dfrac{104}{9}-\dfrac{143}{3}\times\dfrac{143}{3}\times\dfrac{143}{3}\times\left(-\dfrac{104}{9}\right)}}{\dfrac{10}{11}}}}=\dfrac{8379844222464}{109937428043002560}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{\dfrac{10}{11}}{\dfrac{115}{2}}+11}{-5-\dfrac{20}{11}-11}}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{104}{9}}}{-\dfrac{104}{9}}}{\dfrac{\dfrac{-\dfrac{104}{9}}{-\dfrac{104}{9}+\dfrac{104}{9}-\dfrac{20449}{9}\times\dfrac{143}{3}\times\left(-\dfrac{104}{9}\right)}}{\dfrac{10}{11}}}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{10}{11}}{\dfrac{115}{2}}+11}{-5-\dfrac{20}{11}-11}}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{104}{9}}}{-\dfrac{104}{9}}}{\dfrac{\dfrac{-\dfrac{104}{9}}{-\dfrac{104}{9}+\dfrac{104}{9}-\dfrac{2924207}{27}\times\left(-\dfrac{104}{9}\right)}}{\dfrac{10}{11}}}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{10}{11}}{\dfrac{115}{2}}+11}{-5-\dfrac{20}{11}-11}}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{104}{9}}}{-\dfrac{104}{9}}}{\dfrac{\dfrac{-\dfrac{104}{9}}{-\dfrac{104}{9}+\dfrac{104}{9}+\dfrac{304117528}{243}}}{\dfrac{10}{11}}}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{10}{11}}{\dfrac{115}{2}}+11}{-5-\dfrac{20}{11}-11}}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{104}{9}}}{-\dfrac{104}{9}}}{\dfrac{\dfrac{-\dfrac{104}{9}}{0+\dfrac{304117528}{243}}}{\dfrac{10}{11}}}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{10}{11}}{\dfrac{115}{2}}+11}{-5-\dfrac{20}{11}-11}}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{104}{9}}}{-\dfrac{104}{9}}}{\dfrac{\dfrac{-\dfrac{104}{9}}{\dfrac{304117528}{243}}}{\dfrac{10}{11}}}}\\&=&\dfrac{\dfrac{\dfrac{4}{253}+11}{-5-\dfrac{20}{11}-11}}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{104}{9}}}{-\dfrac{104}{9}}}{\dfrac{\dfrac{-\dfrac{104}{9}}{\dfrac{304117528}{243}}}{\dfrac{10}{11}}}}\\&=&\dfrac{\dfrac{\dfrac{4}{253}+11}{-5-\dfrac{20}{11}-11}}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{104}{9}}}{-\dfrac{104}{9}}}{\dfrac{-\dfrac{25272}{2737057752}}{\dfrac{10}{11}}}}\\&=&\dfrac{\dfrac{\dfrac{4}{253}+11}{-5-\dfrac{20}{11}-11}}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{104}{9}}}{-\dfrac{104}{9}}}{-\dfrac{277992}{27370577520}}}\\&=&\dfrac{\dfrac{\dfrac{2787}{253}}{-5-\dfrac{20}{11}-11}}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{104}{9}}}{-\dfrac{104}{9}}}{-\dfrac{277992}{27370577520}}}\\&=&\dfrac{\dfrac{\dfrac{2787}{253}}{-\dfrac{75}{11}-11}}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{104}{9}}}{-\dfrac{104}{9}}}{-\dfrac{277992}{27370577520}}}\\&=&\dfrac{\dfrac{\dfrac{2787}{253}}{-\dfrac{196}{11}}}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{104}{9}}}{-\dfrac{104}{9}}}{-\dfrac{277992}{27370577520}}}\\&=&\dfrac{\dfrac{\dfrac{2787}{253}}{-\dfrac{196}{11}}}{\dfrac{\dfrac{-\dfrac{99}{104}}{-\dfrac{104}{9}}}{-\dfrac{277992}{27370577520}}}\\&=&\dfrac{\dfrac{\dfrac{2787}{253}}{-\dfrac{196}{11}}}{\dfrac{\dfrac{891}{10816}}{-\dfrac{277992}{27370577520}}}\\&=&\dfrac{\dfrac{\dfrac{2787}{253}}{-\dfrac{196}{11}}}{-\dfrac{24387184570320}{3006761472}}\\&=&\dfrac{-\dfrac{2787}{4508}}{-\dfrac{24387184570320}{3006761472}}\\&=&\dfrac{8379844222464}{109937428043002560}\\
\end{eqnarray*}