L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Calculer \[\left(-\dfrac{13}{2}\right)\times\left(\dfrac{61}{10}-\left(7-\left(-\dfrac{79}{2}+10-11-\dfrac{61}{7}-\dfrac{27}{10}\right)-\left(-\dfrac{13}{2}-\dfrac{13}{9}\right)-\left(\dfrac{59}{7}+\dfrac{10}{\dfrac{13}{9}}-\dfrac{61}{7}-\dfrac{61}{7}\right)\right)-10\right)\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\]
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Exercice
On a \( X=\left(-\dfrac{13}{2}\right)\times\left(\dfrac{61}{10}-\left(7-\left(-\dfrac{79}{2}+10-11-\dfrac{61}{7}-\dfrac{27}{10}\right)-\left(-\dfrac{13}{2}-\dfrac{13}{9}\right)-\left(\dfrac{59}{7}+\dfrac{10}{\dfrac{13}{9}}-\dfrac{61}{7}-\dfrac{61}{7}\right)\right)-10\right)\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)=\dfrac{2535227}{42}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-\dfrac{13}{2}\right)\times\left(\dfrac{61}{10}-\left(7-\left(-\dfrac{59}{2}-11-\dfrac{61}{7}-\dfrac{27}{10}\right)-\left(-\dfrac{13}{2}-\dfrac{13}{9}\right)-\left(\dfrac{59}{7}+\dfrac{10}{\dfrac{13}{9}}-\dfrac{61}{7}-\dfrac{61}{7}\right)\right)-10\right)\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\\&=&\left(-\dfrac{13}{2}\right)\times\left(\dfrac{61}{10}-\left(7-\left(-\dfrac{81}{2}-\dfrac{61}{7}-\dfrac{27}{10}\right)-\left(-\dfrac{13}{2}-\dfrac{13}{9}\right)-\left(\dfrac{59}{7}+\dfrac{10}{\dfrac{13}{9}}-\dfrac{61}{7}-\dfrac{61}{7}\right)\right)-10\right)\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\\&=&\left(-\dfrac{13}{2}\right)\times\left(\dfrac{61}{10}-\left(7-\left(-\dfrac{689}{14}-\dfrac{27}{10}\right)-\left(-\dfrac{13}{2}-\dfrac{13}{9}\right)-\left(\dfrac{59}{7}+\dfrac{10}{\dfrac{13}{9}}-\dfrac{61}{7}-\dfrac{61}{7}\right)\right)-10\right)\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\\&=&\left(-\dfrac{13}{2}\right)\times\left(\dfrac{61}{10}-\left(7-\left(-\dfrac{689}{14}-\dfrac{27}{10}\right)-\left(-\dfrac{13}{2}-\dfrac{13}{9}\right)-\left(\dfrac{59}{7}+\dfrac{90}{13}-\dfrac{61}{7}-\dfrac{61}{7}\right)\right)-10\right)\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\\&=&\left(-\dfrac{13}{2}\right)\times\left(\dfrac{61}{10}-\left(7+\dfrac{1817}{35}-\left(-\dfrac{13}{2}-\dfrac{13}{9}\right)-\left(\dfrac{59}{7}+\dfrac{90}{13}-\dfrac{61}{7}-\dfrac{61}{7}\right)\right)-10\right)\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\\&=&\left(-\dfrac{13}{2}\right)\times\left(\dfrac{61}{10}-\left(7+\dfrac{1817}{35}+\dfrac{143}{18}-\left(\dfrac{59}{7}+\dfrac{90}{13}-\dfrac{61}{7}-\dfrac{61}{7}\right)\right)-10\right)\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\\&=&\left(-\dfrac{13}{2}\right)\times\left(\dfrac{61}{10}-\left(7+\dfrac{1817}{35}+\dfrac{143}{18}-\left(\dfrac{1397}{91}-\dfrac{61}{7}-\dfrac{61}{7}\right)\right)-10\right)\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\\&=&\left(-\dfrac{13}{2}\right)\times\left(\dfrac{61}{10}-\left(7+\dfrac{1817}{35}+\dfrac{143}{18}-\left(\dfrac{604}{91}-\dfrac{61}{7}\right)\right)-10\right)\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\\&=&\left(-\dfrac{13}{2}\right)\times\left(\dfrac{61}{10}-\left(7+\dfrac{1817}{35}+\dfrac{143}{18}+\dfrac{27}{13}\right)-10\right)\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\\&=&\left(-\dfrac{13}{2}\right)\times\left(\dfrac{61}{10}-\left(\dfrac{2062}{35}+\dfrac{143}{18}+\dfrac{27}{13}\right)-10\right)\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\\&=&\left(-\dfrac{13}{2}\right)\times\left(\dfrac{61}{10}-\left(\dfrac{42121}{630}+\dfrac{27}{13}\right)-10\right)\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\\&=&\left(-\dfrac{13}{2}\right)\times\left(\dfrac{61}{10}-\dfrac{564583}{8190}-10\right)\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\\&=&\left(-\dfrac{13}{2}\right)\times\left(-\dfrac{257312}{4095}-10\right)\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\\&=&\left(-\dfrac{13}{2}\right)\times-\dfrac{298262}{4095}\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\\&=&\dfrac{149131}{315}\times\left(-10\right)\times\left(-\dfrac{51}{4}\right)\\&=&\left(-\dfrac{298262}{63}\right)\times\left(-\dfrac{51}{4}\right)\\&=&\dfrac{2535227}{42}\\
\end{eqnarray*}