L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6+2-11+4+11}{\dfrac{\dfrac{\dfrac{-2}{\dfrac{41}{2}}}{\dfrac{41}{2}}}{-\dfrac{50}{3}}\times\left(-4\right)\times\left(-2\right)\times\left(-4\right)\times6\times5}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\left(-7+\dfrac{46}{5}-2\right)}}{11}}{-2}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6+2-11+4+11}{\dfrac{\dfrac{\dfrac{-2}{\dfrac{41}{2}}}{\dfrac{41}{2}}}{-\dfrac{50}{3}}\times\left(-4\right)\times\left(-2\right)\times\left(-4\right)\times6\times5}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\left(-7+\dfrac{46}{5}-2\right)}}{11}}{-2}=-\dfrac{210125}{1951488}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6+2-11+4+11}{\dfrac{\dfrac{-\dfrac{4}{41}}{\dfrac{41}{2}}}{-\dfrac{50}{3}}\times\left(-4\right)\times\left(-2\right)\times\left(-4\right)\times6\times5}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\left(-7+\dfrac{46}{5}-2\right)}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6+2-11+4+11}{\dfrac{-\dfrac{8}{1681}}{-\dfrac{50}{3}}\times\left(-4\right)\times\left(-2\right)\times\left(-4\right)\times6\times5}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\left(-7+\dfrac{46}{5}-2\right)}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6+2-11+4+11}{\dfrac{12}{42025}\times\left(-4\right)\times\left(-2\right)\times\left(-4\right)\times6\times5}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\left(-7+\dfrac{46}{5}-2\right)}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6-9+4+11}{\dfrac{12}{42025}\times\left(-4\right)\times\left(-2\right)\times\left(-4\right)\times6\times5}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\left(-7+\dfrac{46}{5}-2\right)}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6-5+11}{\dfrac{12}{42025}\times\left(-4\right)\times\left(-2\right)\times\left(-4\right)\times6\times5}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\left(-7+\dfrac{46}{5}-2\right)}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6+6}{\dfrac{12}{42025}\times\left(-4\right)\times\left(-2\right)\times\left(-4\right)\times6\times5}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\left(-7+\dfrac{46}{5}-2\right)}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6+6}{\left(-\dfrac{48}{42025}\right)\times\left(-2\right)\times\left(-4\right)\times6\times5}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\left(-7+\dfrac{46}{5}-2\right)}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6+6}{\dfrac{96}{42025}\times\left(-4\right)\times6\times5}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\left(-7+\dfrac{46}{5}-2\right)}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6+6}{\dfrac{96}{42025}\times\left(-4\right)\times6\times5}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\left(\dfrac{11}{5}-2\right)}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6+6}{\dfrac{96}{42025}\times\left(-4\right)\times6\times5}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\dfrac{1}{5}}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{12}{\dfrac{96}{42025}\times\left(-4\right)\times6\times5}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\dfrac{1}{5}}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{12}{\left(-\dfrac{384}{42025}\right)\times6\times5}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\dfrac{1}{5}}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{12}{\left(-\dfrac{2304}{42025}\right)\times5}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\dfrac{1}{5}}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{12}{-\dfrac{2304}{8405}}}{2+2+\dfrac{46}{5}}}{\left(-7\right)\times\dfrac{1}{5}}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{12}{-\dfrac{2304}{8405}}}{4+\dfrac{46}{5}}}{\left(-7\right)\times\dfrac{1}{5}}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{12}{-\dfrac{2304}{8405}}}{\dfrac{66}{5}}}{\left(-7\right)\times\dfrac{1}{5}}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{12}{-\dfrac{2304}{8405}}}{\dfrac{66}{5}}}{-\dfrac{7}{5}}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{8405}{192}}{\dfrac{66}{5}}}{-\dfrac{7}{5}}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{42025}{12672}}{-\dfrac{7}{5}}}{11}}{-2}\\&=&\dfrac{\dfrac{\dfrac{210125}{88704}}{11}}{-2}\\&=&\dfrac{\dfrac{210125}{975744}}{-2}\\&=&-\dfrac{210125}{1951488}\\
\end{eqnarray*}