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Exercice

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 \[\dfrac{\dfrac{-2}{\left(-11\right)\times\dfrac{61}{4}}}{\dfrac{61}{4}}\times\left(-\dfrac{43}{6}\right)\times\left(-2-\left(\left(-\dfrac{75}{8}-\dfrac{27}{5}+\dfrac{61}{4}+\dfrac{61}{4}\right)+\dfrac{75}{8}-\dfrac{61}{4}\times\left(-\dfrac{125}{12}\right)\times\left(-\dfrac{73}{3}\right)\right)-\left(9\times\left(-11\right)+\dfrac{27}{2}-\dfrac{75}{8}-11+\dfrac{75}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{\dfrac{-2}{\left(-11\right)\times\dfrac{61}{4}}}{\dfrac{61}{4}}\times\left(-\dfrac{43}{6}\right)\times\left(-2-\left(\left(-\dfrac{75}{8}-\dfrac{27}{5}+\dfrac{61}{4}+\dfrac{61}{4}\right)+\dfrac{75}{8}-\dfrac{61}{4}\times\left(-\dfrac{125}{12}\right)\times\left(-\dfrac{73}{3}\right)\right)-\left(9\times\left(-11\right)+\dfrac{27}{2}-\dfrac{75}{8}-11+\dfrac{75}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)=\dfrac{20180631468270}{3315411000}\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{-2}{-\dfrac{671}{4}}}{\dfrac{61}{4}}\times\left(-\dfrac{43}{6}\right)\times\left(-2-\left(\left(-\dfrac{75}{8}-\dfrac{27}{5}+\dfrac{61}{4}+\dfrac{61}{4}\right)+\dfrac{75}{8}-\dfrac{61}{4}\times\left(-\dfrac{125}{12}\right)\times\left(-\dfrac{73}{3}\right)\right)-\left(9\times\left(-11\right)+\dfrac{27}{2}-\dfrac{75}{8}-11+\dfrac{75}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\dfrac{\dfrac{-2}{-\dfrac{671}{4}}}{\dfrac{61}{4}}\times\left(-\dfrac{43}{6}\right)\times\left(-2-\left(\left(-\dfrac{591}{40}+\dfrac{61}{4}+\dfrac{61}{4}\right)+\dfrac{75}{8}-\dfrac{61}{4}\times\left(-\dfrac{125}{12}\right)\times\left(-\dfrac{73}{3}\right)\right)-\left(9\times\left(-11\right)+\dfrac{27}{2}-\dfrac{75}{8}-11+\dfrac{75}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\dfrac{\dfrac{-2}{-\dfrac{671}{4}}}{\dfrac{61}{4}}\times\left(-\dfrac{43}{6}\right)\times\left(-2-\left(\left(\dfrac{19}{40}+\dfrac{61}{4}\right)+\dfrac{75}{8}-\dfrac{61}{4}\times\left(-\dfrac{125}{12}\right)\times\left(-\dfrac{73}{3}\right)\right)-\left(9\times\left(-11\right)+\dfrac{27}{2}-\dfrac{75}{8}-11+\dfrac{75}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\dfrac{\dfrac{-2}{-\dfrac{671}{4}}}{\dfrac{61}{4}}\times\left(-\dfrac{43}{6}\right)\times\left(-2-\left(\dfrac{629}{40}+\dfrac{75}{8}-\dfrac{61}{4}\times\left(-\dfrac{125}{12}\right)\times\left(-\dfrac{73}{3}\right)\right)-\left(9\times\left(-11\right)+\dfrac{27}{2}-\dfrac{75}{8}-11+\dfrac{75}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\dfrac{\dfrac{-2}{-\dfrac{671}{4}}}{\dfrac{61}{4}}\times\left(-\dfrac{43}{6}\right)\times\left(-2-\left(\dfrac{629}{40}+\dfrac{75}{8}-\left(-\dfrac{7625}{48}\right)\times\left(-\dfrac{73}{3}\right)\right)-\left(9\times\left(-11\right)+\dfrac{27}{2}-\dfrac{75}{8}-11+\dfrac{75}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\dfrac{\dfrac{-2}{-\dfrac{671}{4}}}{\dfrac{61}{4}}\times\left(-\dfrac{43}{6}\right)\times\left(-2-\left(\dfrac{629}{40}+\dfrac{75}{8}-\dfrac{556625}{144}\right)-\left(9\times\left(-11\right)+\dfrac{27}{2}-\dfrac{75}{8}-11+\dfrac{75}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\dfrac{\dfrac{-2}{-\dfrac{671}{4}}}{\dfrac{61}{4}}\times\left(-\dfrac{43}{6}\right)\times\left(-2-\left(\dfrac{629}{40}+\dfrac{75}{8}-\dfrac{556625}{144}\right)-\left(-99+\dfrac{27}{2}-\dfrac{75}{8}-11+\dfrac{75}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\dfrac{\dfrac{-2}{-\dfrac{671}{4}}}{\dfrac{61}{4}}\times\left(-\dfrac{43}{6}\right)\times\left(-2-\left(\dfrac{629}{40}+\dfrac{75}{8}-\dfrac{556625}{144}\right)-\left(-99+\dfrac{27}{2}-\dfrac{75}{8}-\dfrac{13}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\dfrac{\dfrac{8}{671}}{\dfrac{61}{4}}\times\left(-\dfrac{43}{6}\right)\times\left(-2-\left(\dfrac{629}{40}+\dfrac{75}{8}-\dfrac{556625}{144}\right)-\left(-99+\dfrac{27}{2}-\dfrac{75}{8}-\dfrac{13}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\dfrac{32}{40931}\times\left(-\dfrac{43}{6}\right)\times\left(-2-\left(\dfrac{629}{40}+\dfrac{75}{8}-\dfrac{556625}{144}\right)-\left(-99+\dfrac{27}{2}-\dfrac{75}{8}-\dfrac{13}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\dfrac{32}{40931}\times\left(-\dfrac{43}{6}\right)\times\left(-2-\left(\dfrac{251}{10}-\dfrac{556625}{144}\right)-\left(-99+\dfrac{27}{2}-\dfrac{75}{8}-\dfrac{13}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\dfrac{32}{40931}\times\left(-\dfrac{43}{6}\right)\times\left(-2+\dfrac{2765053}{720}-\left(-99+\dfrac{27}{2}-\dfrac{75}{8}-\dfrac{13}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\dfrac{32}{40931}\times\left(-\dfrac{43}{6}\right)\times\left(-2+\dfrac{2765053}{720}-\left(-\dfrac{171}{2}-\dfrac{75}{8}-\dfrac{13}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\dfrac{32}{40931}\times\left(-\dfrac{43}{6}\right)\times\left(-2+\dfrac{2765053}{720}-\left(-\dfrac{759}{8}-\dfrac{13}{8}\right)-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\dfrac{32}{40931}\times\left(-\dfrac{43}{6}\right)\times\left(-2+\dfrac{2765053}{720}+\dfrac{193}{2}-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{75}{8}-2}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\dfrac{32}{40931}\times\left(-\dfrac{43}{6}\right)\times\left(-2+\dfrac{2765053}{720}+\dfrac{193}{2}-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{91}{8}}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\left(-\dfrac{688}{122793}\right)\times\left(-2+\dfrac{2765053}{720}+\dfrac{193}{2}-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{91}{8}}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\left(-\dfrac{688}{122793}\right)\times\left(\dfrac{2763613}{720}+\dfrac{193}{2}-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{91}{8}}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\left(-\dfrac{688}{122793}\right)\times\left(\dfrac{2833093}{720}-\dfrac{62}{3}\right)\times\dfrac{61}{4}\times\dfrac{-\dfrac{91}{8}}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\left(-\dfrac{688}{122793}\right)\times\dfrac{2818213}{720}\times\dfrac{61}{4}\times\dfrac{-\dfrac{91}{8}}{-\dfrac{75}{8}}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\left(-\dfrac{688}{122793}\right)\times\dfrac{2818213}{720}\times\dfrac{61}{4}\times\dfrac{91}{75}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\left(-\dfrac{121183159}{5525685}\right)\times\dfrac{61}{4}\times\dfrac{91}{75}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\left(-\dfrac{7392172699}{22102740}\right)\times\dfrac{91}{75}\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\left(-\dfrac{672687715609}{1657705500}\right)\times\left(-10\right)\times\left(\dfrac{27}{2}-2-10\right)\\&=&\left(-\dfrac{672687715609}{1657705500}\right)\times\left(-10\right)\times\left(\dfrac{23}{2}-10\right)\\&=&\left(-\dfrac{672687715609}{1657705500}\right)\times\left(-10\right)\times\dfrac{3}{2}\\&=&\dfrac{6726877156090}{1657705500}\times\dfrac{3}{2}\\&=&\dfrac{20180631468270}{3315411000}\\ \end{eqnarray*}