L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[-4-\dfrac{\dfrac{\dfrac{-4}{\dfrac{18}{11}\times\left(-\dfrac{131}{7}\right)\times\dfrac{\dfrac{9}{1}}{-\dfrac{131}{7}}\times\left(-\dfrac{8}{7}\right)+\dfrac{8}{7}-\dfrac{\dfrac{\dfrac{18}{11}}{6}}{6}\times1\times1\times9+10}}{7}}{\left(-\dfrac{131}{7}-9-10-1\right)-10-\dfrac{-\dfrac{8}{7}}{-4-10+\dfrac{8}{7}}-1}-\left(-10+9+9\right)\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=-4-\dfrac{\dfrac{\dfrac{-4}{\dfrac{18}{11}\times\left(-\dfrac{131}{7}\right)\times\dfrac{\dfrac{9}{1}}{-\dfrac{131}{7}}\times\left(-\dfrac{8}{7}\right)+\dfrac{8}{7}-\dfrac{\dfrac{\dfrac{18}{11}}{6}}{6}\times1\times1\times9+10}}{7}}{\left(-\dfrac{131}{7}-9-10-1\right)-10-\dfrac{-\dfrac{8}{7}}{-4-10+\dfrac{8}{7}}-1}-\left(-10+9+9\right)=-\dfrac{7364361}{613793}\) . Voici le détail :
\begin{eqnarray*}
X &=&-4-\dfrac{\dfrac{\dfrac{-4}{\dfrac{18}{11}\times\left(-\dfrac{131}{7}\right)\times\dfrac{9}{-\dfrac{131}{7}}\times\left(-\dfrac{8}{7}\right)+\dfrac{8}{7}-\dfrac{\dfrac{\dfrac{18}{11}}{6}}{6}\times1\times1\times9+10}}{7}}{\left(-\dfrac{131}{7}-9-10-1\right)-10-\dfrac{-\dfrac{8}{7}}{-4-10+\dfrac{8}{7}}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{\dfrac{18}{11}\times\left(-\dfrac{131}{7}\right)\times\left(-\dfrac{63}{131}\right)\times\left(-\dfrac{8}{7}\right)+\dfrac{8}{7}-\dfrac{\dfrac{\dfrac{18}{11}}{6}}{6}\times1\times1\times9+10}}{7}}{\left(-\dfrac{131}{7}-9-10-1\right)-10-\dfrac{-\dfrac{8}{7}}{-4-10+\dfrac{8}{7}}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{\dfrac{18}{11}\times\left(-\dfrac{131}{7}\right)\times\left(-\dfrac{63}{131}\right)\times\left(-\dfrac{8}{7}\right)+\dfrac{8}{7}-\dfrac{\dfrac{3}{11}}{6}\times1\times1\times9+10}}{7}}{\left(-\dfrac{131}{7}-9-10-1\right)-10-\dfrac{-\dfrac{8}{7}}{-4-10+\dfrac{8}{7}}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{\dfrac{18}{11}\times\left(-\dfrac{131}{7}\right)\times\left(-\dfrac{63}{131}\right)\times\left(-\dfrac{8}{7}\right)+\dfrac{8}{7}-\dfrac{1}{22}\times1\times1\times9+10}}{7}}{\left(-\dfrac{131}{7}-9-10-1\right)-10-\dfrac{-\dfrac{8}{7}}{-4-10+\dfrac{8}{7}}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{\dfrac{18}{11}\times\left(-\dfrac{131}{7}\right)\times\left(-\dfrac{63}{131}\right)\times\left(-\dfrac{8}{7}\right)+\dfrac{8}{7}-\dfrac{1}{22}\times1\times1\times9+10}}{7}}{\left(-\dfrac{131}{7}-9-10-1\right)-10-\dfrac{-\dfrac{8}{7}}{-14+\dfrac{8}{7}}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{\dfrac{18}{11}\times\left(-\dfrac{131}{7}\right)\times\left(-\dfrac{63}{131}\right)\times\left(-\dfrac{8}{7}\right)+\dfrac{8}{7}-\dfrac{1}{22}\times1\times1\times9+10}}{7}}{\left(-\dfrac{131}{7}-9-10-1\right)-10-\dfrac{-\dfrac{8}{7}}{-\dfrac{90}{7}}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{\left(-\dfrac{2358}{77}\right)\times\left(-\dfrac{63}{131}\right)\times\left(-\dfrac{8}{7}\right)+\dfrac{8}{7}-\dfrac{1}{22}\times1\times1\times9+10}}{7}}{\left(-\dfrac{131}{7}-9-10-1\right)-10-\dfrac{-\dfrac{8}{7}}{-\dfrac{90}{7}}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{\dfrac{162}{11}\times\left(-\dfrac{8}{7}\right)+\dfrac{8}{7}-\dfrac{1}{22}\times1\times1\times9+10}}{7}}{\left(-\dfrac{131}{7}-9-10-1\right)-10-\dfrac{-\dfrac{8}{7}}{-\dfrac{90}{7}}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{-\dfrac{1296}{77}+\dfrac{8}{7}-\dfrac{1}{22}\times1\times1\times9+10}}{7}}{\left(-\dfrac{131}{7}-9-10-1\right)-10-\dfrac{-\dfrac{8}{7}}{-\dfrac{90}{7}}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{-\dfrac{1296}{77}+\dfrac{8}{7}-\dfrac{1}{22}\times1\times9+10}}{7}}{\left(-\dfrac{131}{7}-9-10-1\right)-10-\dfrac{-\dfrac{8}{7}}{-\dfrac{90}{7}}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{-\dfrac{1296}{77}+\dfrac{8}{7}-\dfrac{1}{22}\times9+10}}{7}}{\left(-\dfrac{131}{7}-9-10-1\right)-10-\dfrac{-\dfrac{8}{7}}{-\dfrac{90}{7}}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{-\dfrac{1296}{77}+\dfrac{8}{7}-\dfrac{9}{22}+10}}{7}}{\left(-\dfrac{131}{7}-9-10-1\right)-10-\dfrac{-\dfrac{8}{7}}{-\dfrac{90}{7}}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{-\dfrac{1296}{77}+\dfrac{8}{7}-\dfrac{9}{22}+10}}{7}}{\left(-\dfrac{194}{7}-10-1\right)-10-\dfrac{-\dfrac{8}{7}}{-\dfrac{90}{7}}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{-\dfrac{1296}{77}+\dfrac{8}{7}-\dfrac{9}{22}+10}}{7}}{\left(-\dfrac{264}{7}-1\right)-10-\dfrac{-\dfrac{8}{7}}{-\dfrac{90}{7}}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{-\dfrac{1296}{77}+\dfrac{8}{7}-\dfrac{9}{22}+10}}{7}}{-\dfrac{271}{7}-10-\dfrac{-\dfrac{8}{7}}{-\dfrac{90}{7}}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{-\dfrac{1296}{77}+\dfrac{8}{7}-\dfrac{9}{22}+10}}{7}}{-\dfrac{271}{7}-10-\dfrac{4}{45}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{-\dfrac{1208}{77}-\dfrac{9}{22}+10}}{7}}{-\dfrac{271}{7}-10-\dfrac{4}{45}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{-\dfrac{2479}{154}+10}}{7}}{-\dfrac{271}{7}-10-\dfrac{4}{45}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{-\dfrac{939}{154}}}{7}}{-\dfrac{271}{7}-10-\dfrac{4}{45}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{-\dfrac{939}{154}}}{7}}{-\dfrac{341}{7}-\dfrac{4}{45}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{-\dfrac{939}{154}}}{7}}{-\dfrac{15373}{315}-1}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{-4}{-\dfrac{939}{154}}}{7}}{-\dfrac{15688}{315}}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{\dfrac{616}{939}}{7}}{-\dfrac{15688}{315}}-\left(-10+9+9\right)\\&=&-4-\dfrac{\dfrac{88}{939}}{-\dfrac{15688}{315}}-\left(-10+9+9\right)\\&=&-4+\dfrac{1155}{613793}-\left(-10+9+9\right)\\&=&-4+\dfrac{1155}{613793}-\left(-1+9\right)\\&=&-4+\dfrac{1155}{613793}-8\\&=&-\dfrac{2454017}{613793}-8\\&=&-\dfrac{7364361}{613793}\\
\end{eqnarray*}