L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Calculer \[\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}-1+\dfrac{5}{4}+0-12+\dfrac{79}{4}+0+\dfrac{\dfrac{-\dfrac{121}{9}}{\dfrac{79}{4}}}{\dfrac{5}{4}}\times\left(-12-\dfrac{142}{3}-10+\dfrac{5}{4}\right)+\dfrac{25}{3}\right)\times\dfrac{\dfrac{5}{4}}{6\times\dfrac{25}{3}}\]
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Exercice
On a \( X=\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}-1+\dfrac{5}{4}+0-12+\dfrac{79}{4}+0+\dfrac{\dfrac{-\dfrac{121}{9}}{\dfrac{79}{4}}}{\dfrac{5}{4}}\times\left(-12-\dfrac{142}{3}-10+\dfrac{5}{4}\right)+\dfrac{25}{3}\right)\times\dfrac{\dfrac{5}{4}}{6\times\dfrac{25}{3}}=\dfrac{4862349232}{3839400}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}-1+\dfrac{5}{4}-12+\dfrac{79}{4}+0+\dfrac{\dfrac{-\dfrac{121}{9}}{\dfrac{79}{4}}}{\dfrac{5}{4}}\times\left(-12-\dfrac{142}{3}-10+\dfrac{5}{4}\right)+\dfrac{25}{3}\right)\times\dfrac{\dfrac{5}{4}}{6\times\dfrac{25}{3}}\\&=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}-1-\dfrac{43}{4}+\dfrac{79}{4}+0+\dfrac{\dfrac{-\dfrac{121}{9}}{\dfrac{79}{4}}}{\dfrac{5}{4}}\times\left(-12-\dfrac{142}{3}-10+\dfrac{5}{4}\right)+\dfrac{25}{3}\right)\times\dfrac{\dfrac{5}{4}}{6\times\dfrac{25}{3}}\\&=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}-1+9+0+\dfrac{\dfrac{-\dfrac{121}{9}}{\dfrac{79}{4}}}{\dfrac{5}{4}}\times\left(-12-\dfrac{142}{3}-10+\dfrac{5}{4}\right)+\dfrac{25}{3}\right)\times\dfrac{\dfrac{5}{4}}{6\times\dfrac{25}{3}}\\&=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}-1+9+0+\dfrac{-\dfrac{484}{711}}{\dfrac{5}{4}}\times\left(-12-\dfrac{142}{3}-10+\dfrac{5}{4}\right)+\dfrac{25}{3}\right)\times\dfrac{\dfrac{5}{4}}{6\times\dfrac{25}{3}}\\&=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}-1+9+0+\left(-\dfrac{1936}{3555}\right)\times\left(-12-\dfrac{142}{3}-10+\dfrac{5}{4}\right)+\dfrac{25}{3}\right)\times\dfrac{\dfrac{5}{4}}{6\times\dfrac{25}{3}}\\&=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}-1+9+0+\left(-\dfrac{1936}{3555}\right)\times\left(-\dfrac{178}{3}-10+\dfrac{5}{4}\right)+\dfrac{25}{3}\right)\times\dfrac{\dfrac{5}{4}}{6\times\dfrac{25}{3}}\\&=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}-1+9+0+\left(-\dfrac{1936}{3555}\right)\times\left(-\dfrac{208}{3}+\dfrac{5}{4}\right)+\dfrac{25}{3}\right)\times\dfrac{\dfrac{5}{4}}{6\times\dfrac{25}{3}}\\&=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}-1+9+0+\left(-\dfrac{1936}{3555}\right)\times-\dfrac{817}{12}+\dfrac{25}{3}\right)\times\dfrac{\dfrac{5}{4}}{6\times\dfrac{25}{3}}\\&=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}+8+0+\left(-\dfrac{1936}{3555}\right)\times-\dfrac{817}{12}+\dfrac{25}{3}\right)\times\dfrac{\dfrac{5}{4}}{6\times\dfrac{25}{3}}\\&=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}+8+0+\dfrac{395428}{10665}+\dfrac{25}{3}\right)\times\dfrac{\dfrac{5}{4}}{6\times\dfrac{25}{3}}\\&=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}+8+\dfrac{395428}{10665}+\dfrac{25}{3}\right)\times\dfrac{\dfrac{5}{4}}{6\times\dfrac{25}{3}}\\&=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}+\dfrac{480748}{10665}+\dfrac{25}{3}\right)\times\dfrac{\dfrac{5}{4}}{6\times\dfrac{25}{3}}\\&=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}+\dfrac{569623}{10665}\right)\times\dfrac{\dfrac{5}{4}}{6\times\dfrac{25}{3}}\\&=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\left(\dfrac{25}{3}+\dfrac{569623}{10665}\right)\times\dfrac{\dfrac{5}{4}}{50}\\&=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\dfrac{658498}{10665}\times\dfrac{\dfrac{5}{4}}{50}\\&=&\left(-\dfrac{52}{3}\right)\times\left(-\dfrac{142}{3}\right)\times\dfrac{658498}{10665}\times\dfrac{1}{40}\\&=&\dfrac{7384}{9}\times\dfrac{658498}{10665}\times\dfrac{1}{40}\\&=&\dfrac{4862349232}{95985}\times\dfrac{1}{40}\\&=&\dfrac{4862349232}{3839400}\\
\end{eqnarray*}