L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(-\dfrac{35}{12}\right)\times\left(-\dfrac{35}{12}\right)\times\dfrac{1}{12}\times\left(-\dfrac{121}{4}\right)-\dfrac{136}{7}+4+\dfrac{\dfrac{\dfrac{-\dfrac{136}{7}+4+\dfrac{107}{3}}{7\times\left(-\dfrac{136}{7}\right)}}{-\dfrac{35}{12}}}{-\dfrac{37}{6}}+\dfrac{35}{12}-\dfrac{1}{2}\]
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Exercice
On a \( X=\left(-\dfrac{35}{12}\right)\times\left(-\dfrac{35}{12}\right)\times\dfrac{1}{12}\times\left(-\dfrac{121}{4}\right)-\dfrac{136}{7}+4+\dfrac{\dfrac{\dfrac{-\dfrac{136}{7}+4+\dfrac{107}{3}}{7\times\left(-\dfrac{136}{7}\right)}}{-\dfrac{35}{12}}}{-\dfrac{37}{6}}+\dfrac{35}{12}-\dfrac{1}{2}=-\dfrac{36279072228}{1052642304}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-\dfrac{35}{12}\right)\times\left(-\dfrac{35}{12}\right)\times\dfrac{1}{12}\times\left(-\dfrac{121}{4}\right)-\dfrac{136}{7}+4+\dfrac{\dfrac{\dfrac{-\dfrac{108}{7}+\dfrac{107}{3}}{7\times\left(-\dfrac{136}{7}\right)}}{-\dfrac{35}{12}}}{-\dfrac{37}{6}}+\dfrac{35}{12}-\dfrac{1}{2}\\&=&\left(-\dfrac{35}{12}\right)\times\left(-\dfrac{35}{12}\right)\times\dfrac{1}{12}\times\left(-\dfrac{121}{4}\right)-\dfrac{136}{7}+4+\dfrac{\dfrac{\dfrac{\dfrac{425}{21}}{7\times\left(-\dfrac{136}{7}\right)}}{-\dfrac{35}{12}}}{-\dfrac{37}{6}}+\dfrac{35}{12}-\dfrac{1}{2}\\&=&\left(-\dfrac{35}{12}\right)\times\left(-\dfrac{35}{12}\right)\times\dfrac{1}{12}\times\left(-\dfrac{121}{4}\right)-\dfrac{136}{7}+4+\dfrac{\dfrac{\dfrac{\dfrac{425}{21}}{-136}}{-\dfrac{35}{12}}}{-\dfrac{37}{6}}+\dfrac{35}{12}-\dfrac{1}{2}\\&=&\left(-\dfrac{35}{12}\right)\times\left(-\dfrac{35}{144}\right)\times\left(-\dfrac{121}{4}\right)-\dfrac{136}{7}+4+\dfrac{\dfrac{\dfrac{\dfrac{425}{21}}{-136}}{-\dfrac{35}{12}}}{-\dfrac{37}{6}}+\dfrac{35}{12}-\dfrac{1}{2}\\&=&\left(-\dfrac{35}{12}\right)\times\left(-\dfrac{35}{144}\right)\times\left(-\dfrac{121}{4}\right)-\dfrac{136}{7}+4+\dfrac{\dfrac{-\dfrac{25}{168}}{-\dfrac{35}{12}}}{-\dfrac{37}{6}}+\dfrac{35}{12}-\dfrac{1}{2}\\&=&\dfrac{1225}{1728}\times\left(-\dfrac{121}{4}\right)-\dfrac{136}{7}+4+\dfrac{\dfrac{-\dfrac{25}{168}}{-\dfrac{35}{12}}}{-\dfrac{37}{6}}+\dfrac{35}{12}-\dfrac{1}{2}\\&=&-\dfrac{148225}{6912}-\dfrac{136}{7}+4+\dfrac{\dfrac{-\dfrac{25}{168}}{-\dfrac{35}{12}}}{-\dfrac{37}{6}}+\dfrac{35}{12}-\dfrac{1}{2}\\&=&-\dfrac{148225}{6912}-\dfrac{136}{7}+4+\dfrac{\dfrac{5}{98}}{-\dfrac{37}{6}}+\dfrac{35}{12}-\dfrac{1}{2}\\&=&-\dfrac{148225}{6912}-\dfrac{136}{7}+4-\dfrac{15}{1813}+\dfrac{35}{12}-\dfrac{1}{2}\\&=&-\dfrac{1977607}{48384}+4-\dfrac{15}{1813}+\dfrac{35}{12}-\dfrac{1}{2}\\&=&-\dfrac{1977607}{48384}+4+\dfrac{63275}{21756}-\dfrac{1}{2}\\&=&-\dfrac{1977607}{48384}+4+\dfrac{52397}{21756}\\&=&-\dfrac{1784071}{48384}+\dfrac{52397}{21756}\\&=&-\dfrac{36279072228}{1052642304}\\
\end{eqnarray*}