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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 \[\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{7}{\dfrac{111}{7}}+\dfrac{133}{5}+\dfrac{\dfrac{69}{4}}{\dfrac{22}{3}}\right)-\left(-\dfrac{104}{3}-8\right)\times12\times12\times\dfrac{111}{7}\times\left(-8-3+\dfrac{123}{5}\right)-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{-\dfrac{117}{2}+\dfrac{117}{2}-\dfrac{\dfrac{\dfrac{123}{5}}{-\dfrac{39}{7}}}{\dfrac{133}{5}}-\left(\dfrac{111}{7}-\dfrac{69}{4}\right)}{-3}}}{\dfrac{111}{7}}}\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{7}{\dfrac{111}{7}}+\dfrac{133}{5}+\dfrac{\dfrac{69}{4}}{\dfrac{22}{3}}\right)-\left(-\dfrac{104}{3}-8\right)\times12\times12\times\dfrac{111}{7}\times\left(-8-3+\dfrac{123}{5}\right)-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{-\dfrac{117}{2}+\dfrac{117}{2}-\dfrac{\dfrac{\dfrac{123}{5}}{-\dfrac{39}{7}}}{\dfrac{133}{5}}-\left(\dfrac{111}{7}-\dfrac{69}{4}\right)}{-3}}}{\dfrac{111}{7}}}=\dfrac{3.0990064647873E+20}{170310763022400}\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{49}{111}+\dfrac{133}{5}+\dfrac{\dfrac{69}{4}}{\dfrac{22}{3}}\right)-\left(-\dfrac{104}{3}-8\right)\times12\times12\times\dfrac{111}{7}\times\left(-8-3+\dfrac{123}{5}\right)-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{-\dfrac{117}{2}+\dfrac{117}{2}-\dfrac{\dfrac{\dfrac{123}{5}}{-\dfrac{39}{7}}}{\dfrac{133}{5}}-\left(\dfrac{111}{7}-\dfrac{69}{4}\right)}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{49}{111}+\dfrac{133}{5}+\dfrac{\dfrac{69}{4}}{\dfrac{22}{3}}\right)+\dfrac{128}{3}\times12\times12\times\dfrac{111}{7}\times\left(-8-3+\dfrac{123}{5}\right)-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{-\dfrac{117}{2}+\dfrac{117}{2}-\dfrac{\dfrac{\dfrac{123}{5}}{-\dfrac{39}{7}}}{\dfrac{133}{5}}-\left(\dfrac{111}{7}-\dfrac{69}{4}\right)}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{49}{111}+\dfrac{133}{5}+\dfrac{\dfrac{69}{4}}{\dfrac{22}{3}}\right)+\dfrac{128}{3}\times12\times12\times\dfrac{111}{7}\times\left(-8-3+\dfrac{123}{5}\right)-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{-\dfrac{117}{2}+\dfrac{117}{2}-\dfrac{-\dfrac{287}{65}}{\dfrac{133}{5}}-\left(\dfrac{111}{7}-\dfrac{69}{4}\right)}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{49}{111}+\dfrac{133}{5}+\dfrac{\dfrac{69}{4}}{\dfrac{22}{3}}\right)+\dfrac{128}{3}\times12\times12\times\dfrac{111}{7}\times\left(-8-3+\dfrac{123}{5}\right)-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{-\dfrac{117}{2}+\dfrac{117}{2}+\dfrac{41}{247}-\left(\dfrac{111}{7}-\dfrac{69}{4}\right)}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{49}{111}+\dfrac{133}{5}+\dfrac{\dfrac{69}{4}}{\dfrac{22}{3}}\right)+\dfrac{128}{3}\times12\times12\times\dfrac{111}{7}\times\left(-8-3+\dfrac{123}{5}\right)-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{-\dfrac{117}{2}+\dfrac{117}{2}+\dfrac{41}{247}+\dfrac{39}{28}}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{15008}{555}+\dfrac{\dfrac{69}{4}}{\dfrac{22}{3}}\right)+\dfrac{128}{3}\times12\times12\times\dfrac{111}{7}\times\left(-8-3+\dfrac{123}{5}\right)-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{-\dfrac{117}{2}+\dfrac{117}{2}+\dfrac{41}{247}+\dfrac{39}{28}}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{15008}{555}+\dfrac{207}{88}\right)+\dfrac{128}{3}\times12\times12\times\dfrac{111}{7}\times\left(-8-3+\dfrac{123}{5}\right)-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{-\dfrac{117}{2}+\dfrac{117}{2}+\dfrac{41}{247}+\dfrac{39}{28}}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{15008}{555}+\dfrac{207}{88}\right)-\left(-512\right)\times12\times\dfrac{111}{7}\times\left(-8-3+\dfrac{123}{5}\right)-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{-\dfrac{117}{2}+\dfrac{117}{2}+\dfrac{41}{247}+\dfrac{39}{28}}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{15008}{555}+\dfrac{207}{88}\right)-\left(-6144\right)\times\dfrac{111}{7}\times\left(-8-3+\dfrac{123}{5}\right)-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{-\dfrac{117}{2}+\dfrac{117}{2}+\dfrac{41}{247}+\dfrac{39}{28}}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{15008}{555}+\dfrac{207}{88}\right)-\left(-6144\right)\times\dfrac{111}{7}\times\left(-11+\dfrac{123}{5}\right)-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{-\dfrac{117}{2}+\dfrac{117}{2}+\dfrac{41}{247}+\dfrac{39}{28}}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{15008}{555}+\dfrac{207}{88}\right)-\left(-6144\right)\times\dfrac{111}{7}\times\dfrac{68}{5}-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{-\dfrac{117}{2}+\dfrac{117}{2}+\dfrac{41}{247}+\dfrac{39}{28}}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{15008}{555}+\dfrac{207}{88}\right)-\left(-6144\right)\times\dfrac{111}{7}\times\dfrac{68}{5}-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{0+\dfrac{41}{247}+\dfrac{39}{28}}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{15008}{555}+\dfrac{207}{88}\right)-\left(-6144\right)\times\dfrac{111}{7}\times\dfrac{68}{5}-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{\dfrac{41}{247}+\dfrac{39}{28}}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\left(-8+\dfrac{111}{7}+\dfrac{15008}{555}+\dfrac{207}{88}\right)-\left(-6144\right)\times\dfrac{111}{7}\times\dfrac{68}{5}-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{\dfrac{10781}{6916}}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\left(\dfrac{55}{7}+\dfrac{15008}{555}+\dfrac{207}{88}\right)-\left(-6144\right)\times\dfrac{111}{7}\times\dfrac{68}{5}-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{\dfrac{10781}{6916}}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\left(\dfrac{135581}{3885}+\dfrac{207}{88}\right)-\left(-6144\right)\times\dfrac{111}{7}\times\dfrac{68}{5}-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{\dfrac{10781}{6916}}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\dfrac{12735323}{341880}-\left(-6144\right)\times\dfrac{111}{7}\times\dfrac{68}{5}-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{\dfrac{10781}{6916}}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\dfrac{12735323}{341880}-\left(-\dfrac{681984}{7}\right)\times\dfrac{68}{5}-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{\dfrac{10781}{6916}}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\dfrac{12735323}{341880}+\dfrac{46374912}{35}-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{\dfrac{\dfrac{10781}{6916}}{-3}}}{\dfrac{111}{7}}}\\&=&\dfrac{\dfrac{12735323}{341880}+\dfrac{46374912}{35}-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{-\dfrac{10781}{20748}}}{\dfrac{111}{7}}}\\&=&\dfrac{\dfrac{15855100650865}{11965800}-\dfrac{111}{7}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{-\dfrac{10781}{20748}}}{\dfrac{111}{7}}}\\&=&\dfrac{\dfrac{110984376352255}{83760600}+\dfrac{39}{7}}{\dfrac{\dfrac{\dfrac{12}{-2}}{-\dfrac{10781}{20748}}}{\dfrac{111}{7}}}\\&=&\dfrac{\dfrac{776893901129185}{586324200}}{\dfrac{\dfrac{\dfrac{12}{-2}}{-\dfrac{10781}{20748}}}{\dfrac{111}{7}}}\\&=&\dfrac{\dfrac{776893901129185}{586324200}}{\dfrac{\dfrac{-6}{-\dfrac{10781}{20748}}}{\dfrac{111}{7}}}\\&=&\dfrac{\dfrac{776893901129185}{586324200}}{\dfrac{\dfrac{124488}{10781}}{\dfrac{111}{7}}}\\&=&\dfrac{\dfrac{776893901129185}{586324200}}{\dfrac{290472}{398897}}\\&=&\dfrac{3.0990064647873E+20}{170310763022400}\\ \end{eqnarray*}