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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 \[\dfrac{11}{6}+\dfrac{22}{3}+\left(7+7+3+3+0\times7\times5\times\dfrac{136}{7}-\dfrac{4}{9}-\dfrac{4}{9}+\dfrac{130}{11}\right)\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{\dfrac{-\dfrac{4}{9}}{7}}{-\dfrac{75}{11}}}{7}-7\times5\times8\times\left(-\dfrac{75}{11}\right)\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{11}{6}+\dfrac{22}{3}+\left(7+7+3+3+0\times7\times5\times\dfrac{136}{7}-\dfrac{4}{9}-\dfrac{4}{9}+\dfrac{130}{11}\right)\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{\dfrac{-\dfrac{4}{9}}{7}}{-\dfrac{75}{11}}}{7}-7\times5\times8\times\left(-\dfrac{75}{11}\right)=\dfrac{78928557401925}{37819608750}\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{11}{6}+\dfrac{22}{3}+\left(14+3+3+0\times7\times5\times\dfrac{136}{7}-\dfrac{4}{9}-\dfrac{4}{9}+\dfrac{130}{11}\right)\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{\dfrac{-\dfrac{4}{9}}{7}}{-\dfrac{75}{11}}}{7}-7\times5\times8\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\left(17+3+0\times7\times5\times\dfrac{136}{7}-\dfrac{4}{9}-\dfrac{4}{9}+\dfrac{130}{11}\right)\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{\dfrac{-\dfrac{4}{9}}{7}}{-\dfrac{75}{11}}}{7}-7\times5\times8\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\left(20+0\times7\times5\times\dfrac{136}{7}-\dfrac{4}{9}-\dfrac{4}{9}+\dfrac{130}{11}\right)\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{\dfrac{-\dfrac{4}{9}}{7}}{-\dfrac{75}{11}}}{7}-7\times5\times8\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\left(20+0\times5\times\dfrac{136}{7}-\dfrac{4}{9}-\dfrac{4}{9}+\dfrac{130}{11}\right)\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{\dfrac{-\dfrac{4}{9}}{7}}{-\dfrac{75}{11}}}{7}-7\times5\times8\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\left(20+0\times\dfrac{136}{7}-\dfrac{4}{9}-\dfrac{4}{9}+\dfrac{130}{11}\right)\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{\dfrac{-\dfrac{4}{9}}{7}}{-\dfrac{75}{11}}}{7}-7\times5\times8\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\left(20+0-\dfrac{4}{9}-\dfrac{4}{9}+\dfrac{130}{11}\right)\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{\dfrac{-\dfrac{4}{9}}{7}}{-\dfrac{75}{11}}}{7}-7\times5\times8\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\left(20+0-\dfrac{8}{9}+\dfrac{130}{11}\right)\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{\dfrac{-\dfrac{4}{9}}{7}}{-\dfrac{75}{11}}}{7}-7\times5\times8\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\left(20+0+\dfrac{1082}{99}\right)\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{\dfrac{-\dfrac{4}{9}}{7}}{-\dfrac{75}{11}}}{7}-7\times5\times8\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\left(20+0+\dfrac{1082}{99}\right)\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{-\dfrac{4}{63}}{-\dfrac{75}{11}}}{7}-7\times5\times8\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\left(20+0+\dfrac{1082}{99}\right)\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{44}{4725}}{7}-7\times5\times8\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\left(20+0+\dfrac{1082}{99}\right)\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{44}{4725}}{7}-35\times8\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\left(20+0+\dfrac{1082}{99}\right)\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{44}{4725}}{7}-280\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\left(20+\dfrac{1082}{99}\right)\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{44}{4725}}{7}-280\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\dfrac{3062}{99}\times5+\dfrac{22}{3}-\dfrac{\dfrac{136}{7}}{-\dfrac{75}{11}}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{44}{4725}}{7}-280\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\dfrac{3062}{99}\times5+\dfrac{22}{3}+\dfrac{1496}{525}-\left(-\dfrac{4}{9}-\dfrac{4}{9}\right)+8-5-\dfrac{\dfrac{44}{4725}}{7}-280\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\dfrac{3062}{99}\times5+\dfrac{22}{3}+\dfrac{1496}{525}+\dfrac{8}{9}+8-5-\dfrac{\dfrac{44}{4725}}{7}-280\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\dfrac{3062}{99}\times5+\dfrac{22}{3}+\dfrac{1496}{525}+\dfrac{8}{9}+8-5-\dfrac{44}{33075}-280\times\left(-\dfrac{75}{11}\right)\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\dfrac{3062}{99}\times5+\dfrac{22}{3}+\dfrac{1496}{525}+\dfrac{8}{9}+8-5-\dfrac{44}{33075}+\dfrac{21000}{11}\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\dfrac{15310}{99}+\dfrac{22}{3}+\dfrac{1496}{525}+\dfrac{8}{9}+8-5-\dfrac{44}{33075}+\dfrac{21000}{11}\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\dfrac{15310}{99}+\dfrac{1782}{175}+\dfrac{8}{9}+8-5-\dfrac{44}{33075}+\dfrac{21000}{11}\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\dfrac{15310}{99}+\dfrac{17438}{1575}+8-5-\dfrac{44}{33075}+\dfrac{21000}{11}\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\dfrac{15310}{99}+\dfrac{17438}{1575}+3-\dfrac{44}{33075}+\dfrac{21000}{11}\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\dfrac{15310}{99}+\dfrac{17438}{1575}+\dfrac{99181}{33075}+\dfrac{21000}{11}\\&=&\dfrac{11}{6}+\dfrac{22}{3}+\dfrac{15310}{99}+\dfrac{17438}{1575}+\dfrac{695665991}{363825}\\&=&\dfrac{11}{6}+\dfrac{16036}{99}+\dfrac{17438}{1575}+\dfrac{695665991}{363825}\\&=&\dfrac{11}{6}+\dfrac{2998118}{17325}+\dfrac{695665991}{363825}\\&=&\dfrac{11}{6}+\dfrac{13143203575425}{6303268125}\\&=&\dfrac{78928557401925}{37819608750}\\ \end{eqnarray*}