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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 \[\dfrac{127}{2}\times\dfrac{4}{9}\times\dfrac{\dfrac{-11-4+7}{7}}{7}\times\left(-7\right)\times\dfrac{7}{-\dfrac{71}{8}}\times8\times\left(-\dfrac{4}{11}\right)\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\dfrac{\dfrac{-\dfrac{29}{3}}{-11}}{-\dfrac{4}{11}}\times\left(-\dfrac{5}{6}-7\right)+7-5\right)\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{127}{2}\times\dfrac{4}{9}\times\dfrac{\dfrac{-11-4+7}{7}}{7}\times\left(-7\right)\times\dfrac{7}{-\dfrac{71}{8}}\times8\times\left(-\dfrac{4}{11}\right)\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\dfrac{\dfrac{-\dfrac{29}{3}}{-11}}{-\dfrac{4}{11}}\times\left(-\dfrac{5}{6}-7\right)+7-5\right)=\dfrac{5728727500248}{40487040}\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{127}{2}\times\dfrac{4}{9}\times\dfrac{\dfrac{-15+7}{7}}{7}\times\left(-7\right)\times\dfrac{7}{-\dfrac{71}{8}}\times8\times\left(-\dfrac{4}{11}\right)\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\dfrac{\dfrac{-\dfrac{29}{3}}{-11}}{-\dfrac{4}{11}}\times\left(-\dfrac{5}{6}-7\right)+7-5\right)\\&=&\dfrac{127}{2}\times\dfrac{4}{9}\times\dfrac{\dfrac{-8}{7}}{7}\times\left(-7\right)\times\dfrac{7}{-\dfrac{71}{8}}\times8\times\left(-\dfrac{4}{11}\right)\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\dfrac{\dfrac{-\dfrac{29}{3}}{-11}}{-\dfrac{4}{11}}\times\left(-\dfrac{5}{6}-7\right)+7-5\right)\\&=&\dfrac{127}{2}\times\dfrac{4}{9}\times\dfrac{\dfrac{-8}{7}}{7}\times\left(-7\right)\times\left(-\dfrac{56}{71}\right)\times8\times\left(-\dfrac{4}{11}\right)\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\dfrac{\dfrac{-\dfrac{29}{3}}{-11}}{-\dfrac{4}{11}}\times\left(-\dfrac{5}{6}-7\right)+7-5\right)\\&=&\dfrac{127}{2}\times\dfrac{4}{9}\times\dfrac{\dfrac{-8}{7}}{7}\times\left(-7\right)\times\left(-\dfrac{56}{71}\right)\times8\times\left(-\dfrac{4}{11}\right)\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\dfrac{\dfrac{29}{33}}{-\dfrac{4}{11}}\times\left(-\dfrac{5}{6}-7\right)+7-5\right)\\&=&\dfrac{127}{2}\times\dfrac{4}{9}\times\dfrac{\dfrac{-8}{7}}{7}\times\left(-7\right)\times\left(-\dfrac{56}{71}\right)\times8\times\left(-\dfrac{4}{11}\right)\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\left(-\dfrac{29}{12}\right)\times\left(-\dfrac{5}{6}-7\right)+7-5\right)\\&=&\dfrac{127}{2}\times\dfrac{4}{9}\times\dfrac{\dfrac{-8}{7}}{7}\times\left(-7\right)\times\left(-\dfrac{56}{71}\right)\times8\times\left(-\dfrac{4}{11}\right)\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\left(-\dfrac{29}{12}\right)\times-\dfrac{47}{6}+7-5\right)\\&=&\dfrac{127}{2}\times\dfrac{4}{9}\times\dfrac{-\dfrac{8}{7}}{7}\times\left(-7\right)\times\left(-\dfrac{56}{71}\right)\times8\times\left(-\dfrac{4}{11}\right)\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\left(-\dfrac{29}{12}\right)\times-\dfrac{47}{6}+7-5\right)\\&=&\dfrac{127}{2}\times\dfrac{4}{9}\times-\dfrac{8}{49}\times\left(-7\right)\times\left(-\dfrac{56}{71}\right)\times8\times\left(-\dfrac{4}{11}\right)\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\left(-\dfrac{29}{12}\right)\times-\dfrac{47}{6}+7-5\right)\\&=&\dfrac{127}{2}\times\dfrac{4}{9}\times-\dfrac{8}{49}\times\dfrac{392}{71}\times8\times\left(-\dfrac{4}{11}\right)\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\left(-\dfrac{29}{12}\right)\times-\dfrac{47}{6}+7-5\right)\\&=&\dfrac{127}{2}\times\dfrac{4}{9}\times-\dfrac{8}{49}\times\dfrac{3136}{71}\times\left(-\dfrac{4}{11}\right)\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\left(-\dfrac{29}{12}\right)\times-\dfrac{47}{6}+7-5\right)\\&=&\dfrac{127}{2}\times\dfrac{4}{9}\times-\dfrac{8}{49}\times\dfrac{3136}{71}\times\left(-\dfrac{4}{11}\right)\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\dfrac{1363}{72}+7-5\right)\\&=&\dfrac{254}{9}\times-\dfrac{8}{49}\times\dfrac{3136}{71}\times\left(-\dfrac{4}{11}\right)\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\dfrac{1363}{72}+7-5\right)\\&=&\dfrac{254}{9}\times\left(-\dfrac{512}{71}\right)\times\left(-\dfrac{4}{11}\right)\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\dfrac{1363}{72}+7-5\right)\\&=&\dfrac{254}{9}\times\dfrac{2048}{781}\times\dfrac{12}{5}-\dfrac{71}{8}+\left(-\dfrac{29}{3}\right)\times\left(-11\right)\times\dfrac{127}{2}\times\left(\dfrac{1363}{72}+7-5\right)\\&=&\dfrac{254}{9}\times\dfrac{2048}{781}\times\dfrac{12}{5}-\dfrac{71}{8}+\dfrac{319}{3}\times\dfrac{127}{2}\times\left(\dfrac{1363}{72}+7-5\right)\\&=&\dfrac{254}{9}\times\dfrac{2048}{781}\times\dfrac{12}{5}-\dfrac{71}{8}+\dfrac{40513}{6}\times\left(\dfrac{1363}{72}+7-5\right)\\&=&\dfrac{254}{9}\times\dfrac{2048}{781}\times\dfrac{12}{5}-\dfrac{71}{8}+\dfrac{40513}{6}\times\left(\dfrac{1867}{72}-5\right)\\&=&\dfrac{254}{9}\times\dfrac{2048}{781}\times\dfrac{12}{5}-\dfrac{71}{8}+\dfrac{40513}{6}\times\dfrac{1507}{72}\\&=&\dfrac{520192}{7029}\times\dfrac{12}{5}-\dfrac{71}{8}+\dfrac{40513}{6}\times\dfrac{1507}{72}\\&=&\dfrac{2080768}{11715}-\dfrac{71}{8}+\dfrac{40513}{6}\times\dfrac{1507}{72}\\&=&\dfrac{2080768}{11715}-\dfrac{71}{8}+\dfrac{61053091}{432}\\&=&\dfrac{15814379}{93720}+\dfrac{61053091}{432}\\&=&\dfrac{5728727500248}{40487040}\\ \end{eqnarray*}