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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 \[\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\left(-\dfrac{41}{4}\right)\times\left(-\dfrac{22}{3}\right)\times\dfrac{89}{3}}{\dfrac{61}{11}+\dfrac{61}{11}+2+2-\dfrac{41}{4}}}{3-10\times\dfrac{25}{2}\times\left(-\dfrac{1}{8}\right)-\dfrac{\dfrac{-10}{-\dfrac{1}{8}}}{\dfrac{125}{2}}-\left(3+6+6\right)}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{22}{3}-2}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}-\left(-7-10\right)-0\times6\times\dfrac{125}{2}}}{3}-\dfrac{1}{8}\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\left(-\dfrac{41}{4}\right)\times\left(-\dfrac{22}{3}\right)\times\dfrac{89}{3}}{\dfrac{61}{11}+\dfrac{61}{11}+2+2-\dfrac{41}{4}}}{3-10\times\dfrac{25}{2}\times\left(-\dfrac{1}{8}\right)-\dfrac{\dfrac{-10}{-\dfrac{1}{8}}}{\dfrac{125}{2}}-\left(3+6+6\right)}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{22}{3}-2}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}-\left(-7-10\right)-0\times6\times\dfrac{125}{2}}}{3}-\dfrac{1}{8}=\dfrac{7674905972602}{151432663536}\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\left(-\dfrac{41}{4}\right)\times\left(-\dfrac{22}{3}\right)\times\dfrac{89}{3}}{\dfrac{122}{11}+2+2-\dfrac{41}{4}}}{3-10\times\dfrac{25}{2}\times\left(-\dfrac{1}{8}\right)-\dfrac{\dfrac{-10}{-\dfrac{1}{8}}}{\dfrac{125}{2}}-\left(3+6+6\right)}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{22}{3}-2}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}-\left(-7-10\right)-0\times6\times\dfrac{125}{2}}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\left(-\dfrac{41}{4}\right)\times\left(-\dfrac{22}{3}\right)\times\dfrac{89}{3}}{\dfrac{122}{11}+2+2-\dfrac{41}{4}}}{3-125\times\left(-\dfrac{1}{8}\right)-\dfrac{\dfrac{-10}{-\dfrac{1}{8}}}{\dfrac{125}{2}}-\left(3+6+6\right)}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{22}{3}-2}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}-\left(-7-10\right)-0\times6\times\dfrac{125}{2}}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\left(-\dfrac{41}{4}\right)\times\left(-\dfrac{22}{3}\right)\times\dfrac{89}{3}}{\dfrac{122}{11}+2+2-\dfrac{41}{4}}}{3+\dfrac{125}{8}-\dfrac{\dfrac{-10}{-\dfrac{1}{8}}}{\dfrac{125}{2}}-\left(3+6+6\right)}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{22}{3}-2}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}-\left(-7-10\right)-0\times6\times\dfrac{125}{2}}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\left(-\dfrac{41}{4}\right)\times\left(-\dfrac{22}{3}\right)\times\dfrac{89}{3}}{\dfrac{122}{11}+2+2-\dfrac{41}{4}}}{3+\dfrac{125}{8}-\dfrac{80}{\dfrac{125}{2}}-\left(3+6+6\right)}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{22}{3}-2}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}-\left(-7-10\right)-0\times6\times\dfrac{125}{2}}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\left(-\dfrac{41}{4}\right)\times\left(-\dfrac{22}{3}\right)\times\dfrac{89}{3}}{\dfrac{122}{11}+2+2-\dfrac{41}{4}}}{3+\dfrac{125}{8}-\dfrac{32}{25}-\left(3+6+6\right)}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{22}{3}-2}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}-\left(-7-10\right)-0\times6\times\dfrac{125}{2}}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\left(-\dfrac{41}{4}\right)\times\left(-\dfrac{22}{3}\right)\times\dfrac{89}{3}}{\dfrac{122}{11}+2+2-\dfrac{41}{4}}}{3+\dfrac{125}{8}-\dfrac{32}{25}-\left(9+6\right)}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{22}{3}-2}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}-\left(-7-10\right)-0\times6\times\dfrac{125}{2}}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\left(-\dfrac{41}{4}\right)\times\left(-\dfrac{22}{3}\right)\times\dfrac{89}{3}}{\dfrac{122}{11}+2+2-\dfrac{41}{4}}}{3+\dfrac{125}{8}-\dfrac{32}{25}-15}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{22}{3}-2}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}-\left(-7-10\right)-0\times6\times\dfrac{125}{2}}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\left(-\dfrac{41}{4}\right)\times\left(-\dfrac{22}{3}\right)\times\dfrac{89}{3}}{\dfrac{122}{11}+2+2-\dfrac{41}{4}}}{3+\dfrac{125}{8}-\dfrac{32}{25}-15}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{28}{3}}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}-\left(-7-10\right)-0\times6\times\dfrac{125}{2}}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\left(-\dfrac{41}{4}\right)\times\left(-\dfrac{22}{3}\right)\times\dfrac{89}{3}}{\dfrac{122}{11}+2+2-\dfrac{41}{4}}}{3+\dfrac{125}{8}-\dfrac{32}{25}-15}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{28}{3}}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}+17-0\times6\times\dfrac{125}{2}}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\left(-\dfrac{41}{4}\right)\times\left(-\dfrac{22}{3}\right)\times\dfrac{89}{3}}{\dfrac{122}{11}+2+2-\dfrac{41}{4}}}{3+\dfrac{125}{8}-\dfrac{32}{25}-15}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{28}{3}}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}+17-0\times\dfrac{125}{2}}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\left(-\dfrac{41}{4}\right)\times\left(-\dfrac{22}{3}\right)\times\dfrac{89}{3}}{\dfrac{122}{11}+2+2-\dfrac{41}{4}}}{3+\dfrac{125}{8}-\dfrac{32}{25}-15}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{28}{3}}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}+17-0}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\dfrac{451}{6}\times\dfrac{89}{3}}{\dfrac{122}{11}+2+2-\dfrac{41}{4}}}{3+\dfrac{125}{8}-\dfrac{32}{25}-15}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{28}{3}}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}+17-0}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\dfrac{40139}{18}}{\dfrac{122}{11}+2+2-\dfrac{41}{4}}}{3+\dfrac{125}{8}-\dfrac{32}{25}-15}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{28}{3}}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}+17-0}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\dfrac{40139}{18}}{\dfrac{144}{11}+2-\dfrac{41}{4}}}{3+\dfrac{125}{8}-\dfrac{32}{25}-15}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{28}{3}}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}+17-0}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\dfrac{40139}{18}}{\dfrac{166}{11}-\dfrac{41}{4}}}{3+\dfrac{125}{8}-\dfrac{32}{25}-15}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{28}{3}}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}+17-0}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\dfrac{40139}{18}}{\dfrac{213}{44}}}{3+\dfrac{125}{8}-\dfrac{32}{25}-15}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{28}{3}}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}+17-0}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\dfrac{40139}{18}}{\dfrac{213}{44}}}{\dfrac{149}{8}-\dfrac{32}{25}-15}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{28}{3}}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}+17-0}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\dfrac{40139}{18}}{\dfrac{213}{44}}}{\dfrac{3469}{200}-15}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{28}{3}}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}+17-0}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\dfrac{40139}{18}}{\dfrac{213}{44}}}{\dfrac{469}{200}}}{6}+\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{28}{3}}{2}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}+17-0}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\dfrac{40139}{18}}{\dfrac{213}{44}}}{\dfrac{469}{200}}}{6}+\dfrac{\dfrac{\dfrac{-\dfrac{14}{3}}{-\dfrac{22}{3}}}{-\dfrac{22}{3}+17-0}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\dfrac{40139}{18}}{\dfrac{213}{44}}}{\dfrac{469}{200}}}{6}+\dfrac{\dfrac{\dfrac{7}{11}}{-\dfrac{22}{3}+17-0}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\dfrac{40139}{18}}{\dfrac{213}{44}}}{\dfrac{469}{200}}}{6}+\dfrac{\dfrac{\dfrac{7}{11}}{\dfrac{29}{3}-0}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{\dfrac{40139}{18}}{\dfrac{213}{44}}}{\dfrac{469}{200}}}{6}+\dfrac{\dfrac{\dfrac{7}{11}}{\dfrac{29}{3}}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{\dfrac{883058}{1917}}{\dfrac{469}{200}}}{6}+\dfrac{\dfrac{\dfrac{7}{11}}{\dfrac{29}{3}}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{\dfrac{176611600}{899073}}{6}+\dfrac{\dfrac{\dfrac{7}{11}}{\dfrac{29}{3}}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{88305800}{2697219}+\dfrac{\dfrac{\dfrac{7}{11}}{\dfrac{29}{3}}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{88305800}{2697219}+\dfrac{\dfrac{21}{319}}{3}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{88305800}{2697219}+\dfrac{7}{319}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{28188430733}{860412861}-\dfrac{1}{8}\\&=&\dfrac{61}{11}+\dfrac{25}{2}+\dfrac{224647033003}{6883302888}\\&=&\dfrac{397}{22}+\dfrac{224647033003}{6883302888}\\&=&\dfrac{7674905972602}{151432663536}\\ \end{eqnarray*}