Ataraxy

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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 \[9\times\dfrac{131}{12}\times\left(\dfrac{\dfrac{\dfrac{-\dfrac{77}{12}}{\dfrac{8}{3}}}{\dfrac{37}{2}}}{5}\times\left(-6+5\right)\times\left(-5\right)-8\right)\times\left(-6\right)\times9\times\left(\dfrac{\dfrac{\dfrac{108}{7}}{\dfrac{8}{3}}}{-\dfrac{55}{9}}\times\left(-\dfrac{91}{8}\right)\times\dfrac{-5}{-\dfrac{103}{6}}\times5+9+6-\dfrac{\dfrac{\dfrac{37}{2}}{5}}{\dfrac{48}{7}}-\left(\dfrac{108}{7}-\dfrac{8}{3}\right)-\dfrac{103}{6}\right)\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=9\times\dfrac{131}{12}\times\left(\dfrac{\dfrac{\dfrac{-\dfrac{77}{12}}{\dfrac{8}{3}}}{\dfrac{37}{2}}}{5}\times\left(-6+5\right)\times\left(-5\right)-8\right)\times\left(-6\right)\times9\times\left(\dfrac{\dfrac{\dfrac{108}{7}}{\dfrac{8}{3}}}{-\dfrac{55}{9}}\times\left(-\dfrac{91}{8}\right)\times\dfrac{-5}{-\dfrac{103}{6}}\times5+9+6-\dfrac{\dfrac{\dfrac{37}{2}}{5}}{\dfrac{48}{7}}-\left(\dfrac{108}{7}-\dfrac{8}{3}\right)-\dfrac{103}{6}\right)=\dfrac{41862228400413}{4507345920}$ . Voici le détail : \begin{eqnarray*} X &=&9\times\dfrac{131}{12}\times\left(\dfrac{\dfrac{-\dfrac{77}{32}}{\dfrac{37}{2}}}{5}\times\left(-6+5\right)\times\left(-5\right)-8\right)\times\left(-6\right)\times9\times\left(\dfrac{\dfrac{\dfrac{108}{7}}{\dfrac{8}{3}}}{-\dfrac{55}{9}}\times\left(-\dfrac{91}{8}\right)\times\dfrac{-5}{-\dfrac{103}{6}}\times5+9+6-\dfrac{\dfrac{\dfrac{37}{2}}{5}}{\dfrac{48}{7}}-\left(\dfrac{108}{7}-\dfrac{8}{3}\right)-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(\dfrac{-\dfrac{77}{592}}{5}\times\left(-6+5\right)\times\left(-5\right)-8\right)\times\left(-6\right)\times9\times\left(\dfrac{\dfrac{\dfrac{108}{7}}{\dfrac{8}{3}}}{-\dfrac{55}{9}}\times\left(-\dfrac{91}{8}\right)\times\dfrac{-5}{-\dfrac{103}{6}}\times5+9+6-\dfrac{\dfrac{\dfrac{37}{2}}{5}}{\dfrac{48}{7}}-\left(\dfrac{108}{7}-\dfrac{8}{3}\right)-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(\left(-\dfrac{77}{2960}\right)\times\left(-6+5\right)\times\left(-5\right)-8\right)\times\left(-6\right)\times9\times\left(\dfrac{\dfrac{\dfrac{108}{7}}{\dfrac{8}{3}}}{-\dfrac{55}{9}}\times\left(-\dfrac{91}{8}\right)\times\dfrac{-5}{-\dfrac{103}{6}}\times5+9+6-\dfrac{\dfrac{\dfrac{37}{2}}{5}}{\dfrac{48}{7}}-\left(\dfrac{108}{7}-\dfrac{8}{3}\right)-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(\left(-\dfrac{77}{2960}\right)\times-1\times\left(-5\right)-8\right)\times\left(-6\right)\times9\times\left(\dfrac{\dfrac{\dfrac{108}{7}}{\dfrac{8}{3}}}{-\dfrac{55}{9}}\times\left(-\dfrac{91}{8}\right)\times\dfrac{-5}{-\dfrac{103}{6}}\times5+9+6-\dfrac{\dfrac{\dfrac{37}{2}}{5}}{\dfrac{48}{7}}-\left(\dfrac{108}{7}-\dfrac{8}{3}\right)-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(\left(-\dfrac{77}{2960}\right)\times-1\times\left(-5\right)-8\right)\times\left(-6\right)\times9\times\left(\dfrac{\dfrac{81}{14}}{-\dfrac{55}{9}}\times\left(-\dfrac{91}{8}\right)\times\dfrac{-5}{-\dfrac{103}{6}}\times5+9+6-\dfrac{\dfrac{\dfrac{37}{2}}{5}}{\dfrac{48}{7}}-\left(\dfrac{108}{7}-\dfrac{8}{3}\right)-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(\left(-\dfrac{77}{2960}\right)\times-1\times\left(-5\right)-8\right)\times\left(-6\right)\times9\times\left(\left(-\dfrac{729}{770}\right)\times\left(-\dfrac{91}{8}\right)\times\dfrac{-5}{-\dfrac{103}{6}}\times5+9+6-\dfrac{\dfrac{\dfrac{37}{2}}{5}}{\dfrac{48}{7}}-\left(\dfrac{108}{7}-\dfrac{8}{3}\right)-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(\left(-\dfrac{77}{2960}\right)\times-1\times\left(-5\right)-8\right)\times\left(-6\right)\times9\times\left(\left(-\dfrac{729}{770}\right)\times\left(-\dfrac{91}{8}\right)\times\dfrac{30}{103}\times5+9+6-\dfrac{\dfrac{\dfrac{37}{2}}{5}}{\dfrac{48}{7}}-\left(\dfrac{108}{7}-\dfrac{8}{3}\right)-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(\left(-\dfrac{77}{2960}\right)\times-1\times\left(-5\right)-8\right)\times\left(-6\right)\times9\times\left(\left(-\dfrac{729}{770}\right)\times\left(-\dfrac{91}{8}\right)\times\dfrac{30}{103}\times5+9+6-\dfrac{\dfrac{37}{10}}{\dfrac{48}{7}}-\left(\dfrac{108}{7}-\dfrac{8}{3}\right)-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(\left(-\dfrac{77}{2960}\right)\times-1\times\left(-5\right)-8\right)\times\left(-6\right)\times9\times\left(\left(-\dfrac{729}{770}\right)\times\left(-\dfrac{91}{8}\right)\times\dfrac{30}{103}\times5+9+6-\dfrac{259}{480}-\left(\dfrac{108}{7}-\dfrac{8}{3}\right)-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(\left(-\dfrac{77}{2960}\right)\times-1\times\left(-5\right)-8\right)\times\left(-6\right)\times9\times\left(\left(-\dfrac{729}{770}\right)\times\left(-\dfrac{91}{8}\right)\times\dfrac{30}{103}\times5+9+6-\dfrac{259}{480}-\dfrac{268}{21}-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(\left(\dfrac{77}{2960}\right)\times\left(-5\right)-8\right)\times\left(-6\right)\times9\times\left(\left(-\dfrac{729}{770}\right)\times\left(-\dfrac{91}{8}\right)\times\dfrac{30}{103}\times5+9+6-\dfrac{259}{480}-\dfrac{268}{21}-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(-\dfrac{77}{592}-8\right)\times\left(-6\right)\times9\times\left(\left(-\dfrac{729}{770}\right)\times\left(-\dfrac{91}{8}\right)\times\dfrac{30}{103}\times5+9+6-\dfrac{259}{480}-\dfrac{268}{21}-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(-\dfrac{77}{592}-8\right)\times\left(-6\right)\times9\times\left(\dfrac{9477}{880}\times\dfrac{30}{103}\times5+9+6-\dfrac{259}{480}-\dfrac{268}{21}-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(-\dfrac{77}{592}-8\right)\times\left(-6\right)\times9\times\left(\dfrac{28431}{9064}\times5+9+6-\dfrac{259}{480}-\dfrac{268}{21}-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(-\dfrac{77}{592}-8\right)\times\left(-6\right)\times9\times\left(\dfrac{142155}{9064}+9+6-\dfrac{259}{480}-\dfrac{268}{21}-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(-\dfrac{77}{592}-8\right)\times\left(-6\right)\times9\times\left(\dfrac{142155}{9064}+15-\dfrac{259}{480}-\dfrac{268}{21}-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(-\dfrac{77}{592}-8\right)\times\left(-6\right)\times9\times\left(\dfrac{142155}{9064}+\dfrac{6941}{480}-\dfrac{268}{21}-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times\left(-\dfrac{77}{592}-8\right)\times\left(-6\right)\times9\times\left(\dfrac{142155}{9064}+\dfrac{5707}{3360}-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times-\dfrac{4813}{592}\times\left(-6\right)\times9\times\left(\dfrac{142155}{9064}+\dfrac{5707}{3360}-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times-\dfrac{4813}{592}\times\left(-6\right)\times9\times\left(\dfrac{66171131}{3806880}-\dfrac{103}{6}\right)\\&=&9\times\dfrac{131}{12}\times-\dfrac{4813}{592}\times\left(-6\right)\times9\times\dfrac{819691}{3806880}\\&=&9\times\dfrac{131}{12}\times\dfrac{14439}{296}\times9\times\dfrac{819691}{3806880}\\&=&9\times\dfrac{131}{12}\times\dfrac{129951}{296}\times\dfrac{819691}{3806880}\\&=&9\times\dfrac{131}{12}\times\dfrac{106519665141}{1126836480}\\&=&\dfrac{393}{4}\times\dfrac{106519665141}{1126836480}\\&=&\dfrac{41862228400413}{4507345920}\\ \end{eqnarray*}