L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
Si vous regénérez la page (F5) les valeurs seront changées.
La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{\dfrac{\dfrac{-11}{\dfrac{144}{11}-2+\dfrac{97}{7}+\left(-11\right)\times\dfrac{97}{7}\times\left(-\dfrac{23}{5}\right)+\dfrac{62}{11}-\dfrac{23}{5}+\dfrac{1}{2}}}{-2}}{-11}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{-11}{\dfrac{144}{11}-2+\dfrac{97}{7}+\left(-11\right)\times\dfrac{97}{7}\times\left(-\dfrac{23}{5}\right)+\dfrac{62}{11}-\dfrac{23}{5}+\dfrac{1}{2}}}{-2}}{-11}=-\dfrac{77}{112059}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{-11}{\dfrac{144}{11}-2+\dfrac{97}{7}+\left(-\dfrac{1067}{7}\right)\times\left(-\dfrac{23}{5}\right)+\dfrac{62}{11}-\dfrac{23}{5}+\dfrac{1}{2}}}{-2}}{-11}\\&=&\dfrac{\dfrac{\dfrac{-11}{\dfrac{144}{11}-2+\dfrac{97}{7}+\dfrac{24541}{35}+\dfrac{62}{11}-\dfrac{23}{5}+\dfrac{1}{2}}}{-2}}{-11}\\&=&\dfrac{\dfrac{\dfrac{-11}{\dfrac{144}{11}-2+\dfrac{25026}{35}+\dfrac{62}{11}-\dfrac{23}{5}+\dfrac{1}{2}}}{-2}}{-11}\\&=&\dfrac{\dfrac{\dfrac{-11}{\dfrac{144}{11}-2+\dfrac{277456}{385}-\dfrac{23}{5}+\dfrac{1}{2}}}{-2}}{-11}\\&=&\dfrac{\dfrac{\dfrac{-11}{\dfrac{144}{11}-2+\dfrac{55137}{77}+\dfrac{1}{2}}}{-2}}{-11}\\&=&\dfrac{\dfrac{\dfrac{-11}{\dfrac{144}{11}+\dfrac{54983}{77}+\dfrac{1}{2}}}{-2}}{-11}\\&=&\dfrac{\dfrac{\dfrac{-11}{\dfrac{144}{11}+\dfrac{110043}{154}}}{-2}}{-11}\\&=&\dfrac{\dfrac{\dfrac{-11}{\dfrac{112059}{154}}}{-2}}{-11}\\&=&\dfrac{\dfrac{-\dfrac{1694}{112059}}{-2}}{-11}\\&=&\dfrac{\dfrac{847}{112059}}{-11}\\&=&-\dfrac{77}{112059}\\
\end{eqnarray*}