L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Calculer \[9\times10\times\left(\dfrac{124}{3}-\dfrac{102}{5}+\dfrac{99}{10}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{99}{10}}{9+0-\dfrac{67}{10}+3+\dfrac{48}{5}+\dfrac{124}{3}-\dfrac{67}{10}-\dfrac{15}{8}}}{\dfrac{48}{5}}}{\dfrac{124}{3}}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=9\times10\times\left(\dfrac{124}{3}-\dfrac{102}{5}+\dfrac{99}{10}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{99}{10}}{9+0-\dfrac{67}{10}+3+\dfrac{48}{5}+\dfrac{124}{3}-\dfrac{67}{10}-\dfrac{15}{8}}}{\dfrac{48}{5}}}{\dfrac{124}{3}}=-\dfrac{4120875}{2836624}\) . Voici le détail :
\begin{eqnarray*}
X &=&9\times10\times\left(\dfrac{124}{3}-\dfrac{102}{5}+\dfrac{99}{10}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{99}{10}}{9+0-\dfrac{37}{10}+\dfrac{48}{5}+\dfrac{124}{3}-\dfrac{67}{10}-\dfrac{15}{8}}}{\dfrac{48}{5}}}{\dfrac{124}{3}}\\&=&9\times10\times\left(\dfrac{124}{3}-\dfrac{102}{5}+\dfrac{99}{10}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{99}{10}}{9-\dfrac{37}{10}+\dfrac{48}{5}+\dfrac{124}{3}-\dfrac{67}{10}-\dfrac{15}{8}}}{\dfrac{48}{5}}}{\dfrac{124}{3}}\\&=&9\times10\times\left(\dfrac{124}{3}-\dfrac{102}{5}+\dfrac{99}{10}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{99}{10}}{9+\dfrac{59}{10}+\dfrac{124}{3}-\dfrac{67}{10}-\dfrac{15}{8}}}{\dfrac{48}{5}}}{\dfrac{124}{3}}\\&=&9\times10\times\left(\dfrac{124}{3}-\dfrac{102}{5}+\dfrac{99}{10}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{99}{10}}{9+\dfrac{1417}{30}-\dfrac{67}{10}-\dfrac{15}{8}}}{\dfrac{48}{5}}}{\dfrac{124}{3}}\\&=&9\times10\times\left(\dfrac{124}{3}-\dfrac{102}{5}+\dfrac{99}{10}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{99}{10}}{\dfrac{1687}{30}-\dfrac{67}{10}-\dfrac{15}{8}}}{\dfrac{48}{5}}}{\dfrac{124}{3}}\\&=&9\times10\times\left(\dfrac{124}{3}-\dfrac{102}{5}+\dfrac{99}{10}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{99}{10}}{\dfrac{743}{15}-\dfrac{15}{8}}}{\dfrac{48}{5}}}{\dfrac{124}{3}}\\&=&9\times10\times\left(\dfrac{124}{3}-\dfrac{102}{5}+\dfrac{99}{10}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{99}{10}}{\dfrac{5719}{120}}}{\dfrac{48}{5}}}{\dfrac{124}{3}}\\&=&9\times10\times\left(\dfrac{314}{15}+\dfrac{99}{10}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{99}{10}}{\dfrac{5719}{120}}}{\dfrac{48}{5}}}{\dfrac{124}{3}}\\&=&9\times10\times\dfrac{185}{6}\times\dfrac{\dfrac{\dfrac{-\dfrac{99}{10}}{\dfrac{5719}{120}}}{\dfrac{48}{5}}}{\dfrac{124}{3}}\\&=&9\times10\times\dfrac{185}{6}\times\dfrac{\dfrac{-\dfrac{1188}{5719}}{\dfrac{48}{5}}}{\dfrac{124}{3}}\\&=&9\times10\times\dfrac{185}{6}\times\dfrac{-\dfrac{495}{22876}}{\dfrac{124}{3}}\\&=&9\times10\times\dfrac{185}{6}\times\left(-\dfrac{1485}{2836624}\right)\\&=&90\times\dfrac{185}{6}\times\left(-\dfrac{1485}{2836624}\right)\\&=&2775\times\left(-\dfrac{1485}{2836624}\right)\\&=&-\dfrac{4120875}{2836624}\\
\end{eqnarray*}