L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[-4+\dfrac{33}{5}\times\left(-\dfrac{31}{5}\right)-\dfrac{31}{5}+\left(-\dfrac{31}{5}-4\right)\times\left(-\dfrac{31}{5}-\dfrac{31}{5}\right)\times\left(-\dfrac{9}{4}\right)-4-\dfrac{31}{5}-\dfrac{31}{5}\]
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Exercice
On a \( X=-4+\dfrac{33}{5}\times\left(-\dfrac{31}{5}\right)-\dfrac{31}{5}+\left(-\dfrac{31}{5}-4\right)\times\left(-\dfrac{31}{5}-\dfrac{31}{5}\right)\times\left(-\dfrac{9}{4}\right)-4-\dfrac{31}{5}-\dfrac{31}{5}=-\dfrac{3521}{10}\) . Voici le détail :
\begin{eqnarray*}
X &=&-4-\dfrac{1023}{25}-\dfrac{31}{5}+\left(-\dfrac{31}{5}-4\right)\times\left(-\dfrac{31}{5}-\dfrac{31}{5}\right)\times\left(-\dfrac{9}{4}\right)-4-\dfrac{31}{5}-\dfrac{31}{5}\\&=&-4-\dfrac{1023}{25}-\dfrac{31}{5}-\dfrac{51}{5}\times\left(-\dfrac{31}{5}-\dfrac{31}{5}\right)\times\left(-\dfrac{9}{4}\right)-4-\dfrac{31}{5}-\dfrac{31}{5}\\&=&-4-\dfrac{1023}{25}-\dfrac{31}{5}-\dfrac{51}{5}\times\left(-\dfrac{62}{5}\right)\times\left(-\dfrac{9}{4}\right)-4-\dfrac{31}{5}-\dfrac{31}{5}\\&=&-\dfrac{1123}{25}-\dfrac{31}{5}-\dfrac{51}{5}\times\left(-\dfrac{62}{5}\right)\times\left(-\dfrac{9}{4}\right)-4-\dfrac{31}{5}-\dfrac{31}{5}\\&=&-\dfrac{1278}{25}-\dfrac{51}{5}\times\left(-\dfrac{62}{5}\right)\times\left(-\dfrac{9}{4}\right)-4-\dfrac{31}{5}-\dfrac{31}{5}\\&=&-\dfrac{1278}{25}+\left(\dfrac{3162}{25}\right)\times\left(-\dfrac{9}{4}\right)-4-\dfrac{31}{5}-\dfrac{31}{5}\\&=&-\dfrac{1278}{25}-\dfrac{14229}{50}-4-\dfrac{31}{5}-\dfrac{31}{5}\\&=&-\dfrac{3357}{10}-4-\dfrac{31}{5}-\dfrac{31}{5}\\&=&-\dfrac{3397}{10}-\dfrac{31}{5}-\dfrac{31}{5}\\&=&-\dfrac{3459}{10}-\dfrac{31}{5}\\&=&-\dfrac{3521}{10}\\
\end{eqnarray*}