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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 \[\left(\left(-\dfrac{79}{6}-8-\dfrac{35}{2}+3\right)\times\left(4+6-\dfrac{79}{6}\right)\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\left(4+\dfrac{35}{2}+\dfrac{79}{6}-5\right)+7+9\right)+\dfrac{19}{5}-7-9-11+4-\dfrac{62}{5}-\dfrac{62}{5}-7-9-7+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\left(\left(-\dfrac{79}{6}-8-\dfrac{35}{2}+3\right)\times\left(4+6-\dfrac{79}{6}\right)\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\left(4+\dfrac{35}{2}+\dfrac{79}{6}-5\right)+7+9\right)+\dfrac{19}{5}-7-9-11+4-\dfrac{62}{5}-\dfrac{62}{5}-7-9-7+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6=-\dfrac{51402101}{540}\) . Voici le détail : \begin{eqnarray*} X &=&\left(\left(-\dfrac{127}{6}-\dfrac{35}{2}+3\right)\times\left(4+6-\dfrac{79}{6}\right)\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\left(4+\dfrac{35}{2}+\dfrac{79}{6}-5\right)+7+9\right)+\dfrac{19}{5}-7-9-11+4-\dfrac{62}{5}-\dfrac{62}{5}-7-9-7+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(\left(-\dfrac{116}{3}+3\right)\times\left(4+6-\dfrac{79}{6}\right)\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\left(4+\dfrac{35}{2}+\dfrac{79}{6}-5\right)+7+9\right)+\dfrac{19}{5}-7-9-11+4-\dfrac{62}{5}-\dfrac{62}{5}-7-9-7+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times\left(4+6-\dfrac{79}{6}\right)\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\left(4+\dfrac{35}{2}+\dfrac{79}{6}-5\right)+7+9\right)+\dfrac{19}{5}-7-9-11+4-\dfrac{62}{5}-\dfrac{62}{5}-7-9-7+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times\left(10-\dfrac{79}{6}\right)\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\left(4+\dfrac{35}{2}+\dfrac{79}{6}-5\right)+7+9\right)+\dfrac{19}{5}-7-9-11+4-\dfrac{62}{5}-\dfrac{62}{5}-7-9-7+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times-\dfrac{19}{6}\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\left(4+\dfrac{35}{2}+\dfrac{79}{6}-5\right)+7+9\right)+\dfrac{19}{5}-7-9-11+4-\dfrac{62}{5}-\dfrac{62}{5}-7-9-7+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times-\dfrac{19}{6}\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\left(\dfrac{43}{2}+\dfrac{79}{6}-5\right)+7+9\right)+\dfrac{19}{5}-7-9-11+4-\dfrac{62}{5}-\dfrac{62}{5}-7-9-7+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times-\dfrac{19}{6}\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\left(\dfrac{104}{3}-5\right)+7+9\right)+\dfrac{19}{5}-7-9-11+4-\dfrac{62}{5}-\dfrac{62}{5}-7-9-7+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times-\dfrac{19}{6}\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\dfrac{89}{3}+7+9\right)+\dfrac{19}{5}-7-9-11+4-\dfrac{62}{5}-\dfrac{62}{5}-7-9-7+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times-\dfrac{19}{6}\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\dfrac{89}{3}+7+9\right)+\dfrac{19}{5}-16-11+4-\dfrac{62}{5}-\dfrac{62}{5}-7-9-7+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times-\dfrac{19}{6}\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\dfrac{89}{3}+7+9\right)+\dfrac{19}{5}-27+4-\dfrac{62}{5}-\dfrac{62}{5}-7-9-7+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times-\dfrac{19}{6}\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\dfrac{89}{3}+7+9\right)+\dfrac{19}{5}-27-\dfrac{42}{5}-\dfrac{62}{5}-7-9-7+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times-\dfrac{19}{6}\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\dfrac{89}{3}+7+9\right)+\dfrac{19}{5}-27-\dfrac{42}{5}-\dfrac{97}{5}-9-7+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times-\dfrac{19}{6}\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\dfrac{89}{3}+7+9\right)+\dfrac{19}{5}-27-\dfrac{42}{5}-\dfrac{142}{5}-7+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times-\dfrac{19}{6}\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\dfrac{89}{3}+7+9\right)+\dfrac{19}{5}-27-\dfrac{42}{5}-\dfrac{177}{5}+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{4-\dfrac{79}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times-\dfrac{19}{6}\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\dfrac{89}{3}+7+9\right)+\dfrac{19}{5}-27-\dfrac{42}{5}-\dfrac{177}{5}+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{-\dfrac{55}{6}}{\left(-\dfrac{62}{5}\right)\times5\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times-\dfrac{19}{6}\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\dfrac{89}{3}+7+9\right)+\dfrac{19}{5}-27-\dfrac{42}{5}-\dfrac{177}{5}+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{-\dfrac{55}{6}}{\left(-62\right)\times\left(-9\right)\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times-\dfrac{19}{6}\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\dfrac{89}{3}+7+9\right)+\dfrac{19}{5}-27-\dfrac{42}{5}-\dfrac{177}{5}+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{-\dfrac{55}{6}}{558\times\left(-11\right)}\right)\times6\\&=&\left(-\dfrac{107}{3}\times-\dfrac{19}{6}\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\dfrac{89}{3}+7+9\right)+\dfrac{19}{5}-27-\dfrac{42}{5}-\dfrac{177}{5}+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{-\dfrac{55}{6}}{-6138}\right)\times6\\&=&\left(\dfrac{2033}{18}\times3\times\left(-\dfrac{79}{6}+7\right)\times\left(\dfrac{89}{3}+7+9\right)+\dfrac{19}{5}-27-\dfrac{42}{5}-\dfrac{177}{5}+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{-\dfrac{55}{6}}{-6138}\right)\times6\\&=&\left(\dfrac{2033}{6}\times\left(-\dfrac{79}{6}+7\right)\times\left(\dfrac{89}{3}+7+9\right)+\dfrac{19}{5}-27-\dfrac{42}{5}-\dfrac{177}{5}+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{-\dfrac{55}{6}}{-6138}\right)\times6\\&=&\left(\dfrac{2033}{6}\times-\dfrac{37}{6}\times\left(\dfrac{89}{3}+7+9\right)+\dfrac{19}{5}-27-\dfrac{42}{5}-\dfrac{177}{5}+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{-\dfrac{55}{6}}{-6138}\right)\times6\\&=&\left(\dfrac{2033}{6}\times-\dfrac{37}{6}\times\left(\dfrac{110}{3}+9\right)+\dfrac{19}{5}-27-\dfrac{42}{5}-\dfrac{177}{5}+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{-\dfrac{55}{6}}{-6138}\right)\times6\\&=&\left(\dfrac{2033}{6}\times-\dfrac{37}{6}\times\dfrac{137}{3}+\dfrac{19}{5}-27-\dfrac{42}{5}-\dfrac{177}{5}+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{-\dfrac{55}{6}}{-6138}\right)\times6\\&=&\left(\dfrac{2033}{6}\times-\dfrac{37}{6}\times\dfrac{137}{3}-\dfrac{116}{5}-\dfrac{42}{5}-\dfrac{177}{5}+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{-\dfrac{55}{6}}{-6138}\right)\times6\\&=&\left(\dfrac{2033}{6}\times-\dfrac{37}{6}\times\dfrac{137}{3}-\dfrac{116}{5}-\dfrac{219}{5}+\dfrac{5}{2}-3-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{-\dfrac{55}{6}}{-6138}\right)\times6\\&=&\left(\dfrac{2033}{6}\times-\dfrac{37}{6}\times\dfrac{137}{3}-\dfrac{116}{5}-\dfrac{219}{5}-\dfrac{1}{2}-9+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{-\dfrac{55}{6}}{-6138}\right)\times6\\&=&\left(\dfrac{2033}{6}\times-\dfrac{37}{6}\times\dfrac{137}{3}-\dfrac{116}{5}-\dfrac{219}{5}-\dfrac{19}{2}+\dfrac{79}{6}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{-\dfrac{55}{6}}{-6138}\right)\times6\\&=&\left(\dfrac{2033}{6}\times-\dfrac{37}{6}\times\dfrac{137}{3}-\dfrac{116}{5}-\dfrac{219}{5}+\dfrac{11}{3}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{-\dfrac{55}{6}}{-6138}\right)\times6\\&=&\left(\dfrac{2033}{6}\times-\dfrac{37}{6}\times\dfrac{137}{3}-\dfrac{116}{5}-\dfrac{219}{5}+\dfrac{11}{3}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{5}{3348}\right)\times6\\&=&\left(-\dfrac{75221}{36}\times\dfrac{137}{3}-\dfrac{116}{5}-\dfrac{219}{5}+\dfrac{11}{3}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{5}{3348}\right)\times6\\&=&\left(-\dfrac{10305277}{108}-\dfrac{116}{5}-\dfrac{219}{5}+\dfrac{11}{3}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{5}{3348}\right)\times6\\&=&\left(-\dfrac{10305277}{108}-67+\dfrac{11}{3}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{5}{3348}\right)\times6\\&=&\left(-\dfrac{10305277}{108}-\dfrac{190}{3}\right)-4-\left(-\dfrac{62}{5}\right)\times\left(4-\dfrac{5}{3348}\right)\times6\\&=&\left(-\dfrac{10305277}{108}-\dfrac{190}{3}\right)-4-\left(-\dfrac{62}{5}\right)\times\dfrac{13387}{3348}\times6\\&=&-\dfrac{10312117}{108}-4-\left(-\dfrac{62}{5}\right)\times\dfrac{13387}{3348}\times6\\&=&-\dfrac{10312117}{108}-4-\left(-\dfrac{13387}{270}\right)\times6\\&=&-\dfrac{10312117}{108}-4+\dfrac{13387}{45}\\&=&-\dfrac{10312549}{108}+\dfrac{13387}{45}\\&=&-\dfrac{51402101}{540}\\ \end{eqnarray*}