L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(\dfrac{21}{2}-1\times\dfrac{21}{2}\times12\times9-\dfrac{59}{4}-\dfrac{59}{4}\right)-\dfrac{\dfrac{\dfrac{-\dfrac{59}{4}}{1\times\dfrac{70}{3}\times9\times2}}{\left(-7\right)\times\dfrac{65}{6}}}{-12}-\dfrac{65}{6}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(\dfrac{21}{2}-1\times\dfrac{21}{2}\times12\times9-\dfrac{59}{4}-\dfrac{59}{4}\right)-\dfrac{\dfrac{\dfrac{-\dfrac{59}{4}}{1\times\dfrac{70}{3}\times9\times2}}{\left(-7\right)\times\dfrac{65}{6}}}{-12}-\dfrac{65}{6}=-\dfrac{10675610046}{9172800}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(\dfrac{21}{2}-1\times126\times9-\dfrac{59}{4}-\dfrac{59}{4}\right)-\dfrac{\dfrac{\dfrac{-\dfrac{59}{4}}{1\times\dfrac{70}{3}\times9\times2}}{\left(-7\right)\times\dfrac{65}{6}}}{-12}-\dfrac{65}{6}\\&=&\left(\dfrac{21}{2}-126\times9-\dfrac{59}{4}-\dfrac{59}{4}\right)-\dfrac{\dfrac{\dfrac{-\dfrac{59}{4}}{1\times\dfrac{70}{3}\times9\times2}}{\left(-7\right)\times\dfrac{65}{6}}}{-12}-\dfrac{65}{6}\\&=&\left(\dfrac{21}{2}-1134-\dfrac{59}{4}-\dfrac{59}{4}\right)-\dfrac{\dfrac{\dfrac{-\dfrac{59}{4}}{1\times\dfrac{70}{3}\times9\times2}}{\left(-7\right)\times\dfrac{65}{6}}}{-12}-\dfrac{65}{6}\\&=&\left(-\dfrac{2247}{2}-\dfrac{59}{4}-\dfrac{59}{4}\right)-\dfrac{\dfrac{\dfrac{-\dfrac{59}{4}}{1\times\dfrac{70}{3}\times9\times2}}{\left(-7\right)\times\dfrac{65}{6}}}{-12}-\dfrac{65}{6}\\&=&\left(-\dfrac{2247}{2}-\dfrac{59}{4}-\dfrac{59}{4}\right)-\dfrac{\dfrac{\dfrac{-\dfrac{59}{4}}{\dfrac{70}{3}\times9\times2}}{\left(-7\right)\times\dfrac{65}{6}}}{-12}-\dfrac{65}{6}\\&=&\left(-\dfrac{2247}{2}-\dfrac{59}{4}-\dfrac{59}{4}\right)-\dfrac{\dfrac{\dfrac{-\dfrac{59}{4}}{210\times2}}{\left(-7\right)\times\dfrac{65}{6}}}{-12}-\dfrac{65}{6}\\&=&\left(-\dfrac{2247}{2}-\dfrac{59}{4}-\dfrac{59}{4}\right)-\dfrac{\dfrac{\dfrac{-\dfrac{59}{4}}{420}}{\left(-7\right)\times\dfrac{65}{6}}}{-12}-\dfrac{65}{6}\\&=&\left(-\dfrac{2247}{2}-\dfrac{59}{4}-\dfrac{59}{4}\right)-\dfrac{\dfrac{\dfrac{-\dfrac{59}{4}}{420}}{-\dfrac{455}{6}}}{-12}-\dfrac{65}{6}\\&=&\left(-\dfrac{4553}{4}-\dfrac{59}{4}\right)-\dfrac{\dfrac{\dfrac{-\dfrac{59}{4}}{420}}{-\dfrac{455}{6}}}{-12}-\dfrac{65}{6}\\&=&-1153-\dfrac{\dfrac{\dfrac{-\dfrac{59}{4}}{420}}{-\dfrac{455}{6}}}{-12}-\dfrac{65}{6}\\&=&-1153-\dfrac{\dfrac{-\dfrac{59}{1680}}{-\dfrac{455}{6}}}{-12}-\dfrac{65}{6}\\&=&-1153-\dfrac{\dfrac{59}{127400}}{-12}-\dfrac{65}{6}\\&=&-1153+\dfrac{59}{1528800}-\dfrac{65}{6}\\&=&-\dfrac{1762706341}{1528800}-\dfrac{65}{6}\\&=&-\dfrac{10675610046}{9172800}\\
\end{eqnarray*}