L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(-9\right)\times\left(2-\dfrac{\dfrac{\dfrac{-\dfrac{93}{4}}{\dfrac{37}{4}\times\left(-\dfrac{11}{7}\right)\times\left(-\dfrac{37}{12}\right)\times\left(-\dfrac{13}{2}\right)}}{2\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{93}{4}\right)}}{\dfrac{4}{5}}-\dfrac{124}{9}+\dfrac{37}{12}\right)\times\dfrac{14}{3}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(-9\right)\times\left(2-\dfrac{\dfrac{\dfrac{-\dfrac{93}{4}}{\dfrac{37}{4}\times\left(-\dfrac{11}{7}\right)\times\left(-\dfrac{37}{12}\right)\times\left(-\dfrac{13}{2}\right)}}{2\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{93}{4}\right)}}{\dfrac{4}{5}}-\dfrac{124}{9}+\dfrac{37}{12}\right)\times\dfrac{14}{3}=\dfrac{428989001}{1174602}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-9\right)\times\left(2-\dfrac{\dfrac{\dfrac{-\dfrac{93}{4}}{\left(-\dfrac{407}{28}\right)\times\left(-\dfrac{37}{12}\right)\times\left(-\dfrac{13}{2}\right)}}{2\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{93}{4}\right)}}{\dfrac{4}{5}}-\dfrac{124}{9}+\dfrac{37}{12}\right)\times\dfrac{14}{3}\\&=&\left(-9\right)\times\left(2-\dfrac{\dfrac{\dfrac{-\dfrac{93}{4}}{\dfrac{15059}{336}\times\left(-\dfrac{13}{2}\right)}}{2\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{93}{4}\right)}}{\dfrac{4}{5}}-\dfrac{124}{9}+\dfrac{37}{12}\right)\times\dfrac{14}{3}\\&=&\left(-9\right)\times\left(2-\dfrac{\dfrac{\dfrac{-\dfrac{93}{4}}{-\dfrac{195767}{672}}}{2\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{93}{4}\right)}}{\dfrac{4}{5}}-\dfrac{124}{9}+\dfrac{37}{12}\right)\times\dfrac{14}{3}\\&=&\left(-9\right)\times\left(2-\dfrac{\dfrac{\dfrac{-\dfrac{93}{4}}{-\dfrac{195767}{672}}}{\left(-\dfrac{10}{3}\right)\times\left(-\dfrac{93}{4}\right)}}{\dfrac{4}{5}}-\dfrac{124}{9}+\dfrac{37}{12}\right)\times\dfrac{14}{3}\\&=&\left(-9\right)\times\left(2-\dfrac{\dfrac{\dfrac{-\dfrac{93}{4}}{-\dfrac{195767}{672}}}{\dfrac{155}{2}}}{\dfrac{4}{5}}-\dfrac{124}{9}+\dfrac{37}{12}\right)\times\dfrac{14}{3}\\&=&\left(-9\right)\times\left(2-\dfrac{\dfrac{\dfrac{15624}{195767}}{\dfrac{155}{2}}}{\dfrac{4}{5}}-\dfrac{124}{9}+\dfrac{37}{12}\right)\times\dfrac{14}{3}\\&=&\left(-9\right)\times\left(2-\dfrac{\dfrac{1008}{978835}}{\dfrac{4}{5}}-\dfrac{124}{9}+\dfrac{37}{12}\right)\times\dfrac{14}{3}\\&=&\left(-9\right)\times\left(2-\dfrac{252}{195767}-\dfrac{124}{9}+\dfrac{37}{12}\right)\times\dfrac{14}{3}\\&=&\left(-9\right)\times\left(\dfrac{391282}{195767}-\dfrac{124}{9}+\dfrac{37}{12}\right)\times\dfrac{14}{3}\\&=&\left(-9\right)\times\left(-\dfrac{20753570}{1761903}+\dfrac{37}{12}\right)\times\dfrac{14}{3}\\&=&\left(-9\right)\times\left(-\dfrac{61284143}{7047612}\right)\times\dfrac{14}{3}\\&=&\dfrac{61284143}{783068}\times\dfrac{14}{3}\\&=&\dfrac{428989001}{1174602}\\
\end{eqnarray*}