L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(-1+6-3+8+7\right)\times\dfrac{-4-\dfrac{143}{8}-\dfrac{52}{3}}{-\dfrac{136}{11}}\times\dfrac{31}{5}\times\dfrac{129}{11}\times\left(4-\left(-3+\dfrac{136}{11}\right)-\dfrac{31}{5}\right)+\dfrac{-8+8+4}{-3}-1\]
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Exercice
On a \( X=\left(-1+6-3+8+7\right)\times\dfrac{-4-\dfrac{143}{8}-\dfrac{52}{3}}{-\dfrac{136}{11}}\times\dfrac{31}{5}\times\dfrac{129}{11}\times\left(4-\left(-3+\dfrac{136}{11}\right)-\dfrac{31}{5}\right)+\dfrac{-8+8+4}{-3}-1=-\dfrac{78983147892}{1742400}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-1+6-3+8+7\right)\times\dfrac{-\dfrac{175}{8}-\dfrac{52}{3}}{-\dfrac{136}{11}}\times\dfrac{31}{5}\times\dfrac{129}{11}\times\left(4-\left(-3+\dfrac{136}{11}\right)-\dfrac{31}{5}\right)+\dfrac{-8+8+4}{-3}-1\\&=&\left(-1+6-3+8+7\right)\times\dfrac{-\dfrac{175}{8}-\dfrac{52}{3}}{-\dfrac{136}{11}}\times\dfrac{31}{5}\times\dfrac{129}{11}\times\left(4-\dfrac{103}{11}-\dfrac{31}{5}\right)+\dfrac{-8+8+4}{-3}-1\\&=&\left(-1+6+5+7\right)\times\dfrac{-\dfrac{175}{8}-\dfrac{52}{3}}{-\dfrac{136}{11}}\times\dfrac{31}{5}\times\dfrac{129}{11}\times\left(4-\dfrac{103}{11}-\dfrac{31}{5}\right)+\dfrac{-8+8+4}{-3}-1\\&=&\left(-1+6+12\right)\times\dfrac{-\dfrac{175}{8}-\dfrac{52}{3}}{-\dfrac{136}{11}}\times\dfrac{31}{5}\times\dfrac{129}{11}\times\left(4-\dfrac{103}{11}-\dfrac{31}{5}\right)+\dfrac{-8+8+4}{-3}-1\\&=&\left(-1+6+12\right)\times\dfrac{-\dfrac{941}{24}}{-\dfrac{136}{11}}\times\dfrac{31}{5}\times\dfrac{129}{11}\times\left(4-\dfrac{103}{11}-\dfrac{31}{5}\right)+\dfrac{-8+8+4}{-3}-1\\&=&\left(-1+6+12\right)\times\dfrac{-\dfrac{941}{24}}{-\dfrac{136}{11}}\times\dfrac{31}{5}\times\dfrac{129}{11}\times\left(-\dfrac{59}{11}-\dfrac{31}{5}\right)+\dfrac{-8+8+4}{-3}-1\\&=&\left(-1+6+12\right)\times\dfrac{-\dfrac{941}{24}}{-\dfrac{136}{11}}\times\dfrac{31}{5}\times\dfrac{129}{11}\times-\dfrac{636}{55}+\dfrac{-8+8+4}{-3}-1\\&=&\left(5+12\right)\times\dfrac{-\dfrac{941}{24}}{-\dfrac{136}{11}}\times\dfrac{31}{5}\times\dfrac{129}{11}\times-\dfrac{636}{55}+\dfrac{-8+8+4}{-3}-1\\&=&17\times\dfrac{-\dfrac{941}{24}}{-\dfrac{136}{11}}\times\dfrac{31}{5}\times\dfrac{129}{11}\times-\dfrac{636}{55}+\dfrac{-8+8+4}{-3}-1\\&=&17\times\left(\dfrac{10351}{3264}\right)\times\dfrac{31}{5}\times\dfrac{129}{11}\times-\dfrac{636}{55}+\dfrac{-8+8+4}{-3}-1\\&=&17\times\left(\dfrac{10351}{3264}\right)\times\dfrac{3999}{55}\times-\dfrac{636}{55}+\dfrac{-8+8+4}{-3}-1\\&=&17\times\left(\dfrac{10351}{3264}\right)\times-\dfrac{2543364}{3025}+\dfrac{-8+8+4}{-3}-1\\&=&17\times\left(\dfrac{10351}{3264}\right)\times-\dfrac{2543364}{3025}+\dfrac{0+4}{-3}-1\\&=&17\times\left(\dfrac{10351}{3264}\right)\times-\dfrac{2543364}{3025}+\dfrac{4}{-3}-1\\&=&\dfrac{10351}{192}\times-\dfrac{2543364}{3025}+\dfrac{4}{-3}-1\\&=&-\dfrac{26326360764}{580800}+\dfrac{4}{-3}-1\\&=&-\dfrac{26326360764}{580800}-\dfrac{4}{3}-1\\&=&-\dfrac{78981405492}{1742400}-1\\&=&-\dfrac{78983147892}{1742400}\\
\end{eqnarray*}