L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
Si vous regénérez la page (F5) les valeurs seront changées.
La correction se trouve en bas de page.
Exercice
Calculer \[-11+\dfrac{119}{3}-\dfrac{\dfrac{-\dfrac{5}{2}}{-1-\dfrac{\dfrac{\dfrac{-\dfrac{66}{5}}{3}}{-\dfrac{125}{2}}}{3}+1+1}}{-\dfrac{125}{2}}\times\left(-\dfrac{125}{2}-\dfrac{105}{4}-\dfrac{\dfrac{-\dfrac{40}{11}}{-\dfrac{40}{11}}}{-1}\times\dfrac{105}{4}-\dfrac{43}{2}\right)+9\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=-11+\dfrac{119}{3}-\dfrac{\dfrac{-\dfrac{5}{2}}{-1-\dfrac{\dfrac{\dfrac{-\dfrac{66}{5}}{3}}{-\dfrac{125}{2}}}{3}+1+1}}{-\dfrac{125}{2}}\times\left(-\dfrac{125}{2}-\dfrac{105}{4}-\dfrac{\dfrac{-\dfrac{40}{11}}{-\dfrac{40}{11}}}{-1}\times\dfrac{105}{4}-\dfrac{43}{2}\right)+9=\dfrac{225803}{5493}\) . Voici le détail :
\begin{eqnarray*}
X &=&-11+\dfrac{119}{3}-\dfrac{\dfrac{-\dfrac{5}{2}}{-1-\dfrac{\dfrac{-\dfrac{22}{5}}{-\dfrac{125}{2}}}{3}+1+1}}{-\dfrac{125}{2}}\times\left(-\dfrac{125}{2}-\dfrac{105}{4}-\dfrac{\dfrac{-\dfrac{40}{11}}{-\dfrac{40}{11}}}{-1}\times\dfrac{105}{4}-\dfrac{43}{2}\right)+9\\&=&-11+\dfrac{119}{3}-\dfrac{\dfrac{-\dfrac{5}{2}}{-1-\dfrac{\dfrac{44}{625}}{3}+1+1}}{-\dfrac{125}{2}}\times\left(-\dfrac{125}{2}-\dfrac{105}{4}-\dfrac{\dfrac{-\dfrac{40}{11}}{-\dfrac{40}{11}}}{-1}\times\dfrac{105}{4}-\dfrac{43}{2}\right)+9\\&=&-11+\dfrac{119}{3}-\dfrac{\dfrac{-\dfrac{5}{2}}{-1-\dfrac{44}{1875}+1+1}}{-\dfrac{125}{2}}\times\left(-\dfrac{125}{2}-\dfrac{105}{4}-\dfrac{\dfrac{-\dfrac{40}{11}}{-\dfrac{40}{11}}}{-1}\times\dfrac{105}{4}-\dfrac{43}{2}\right)+9\\&=&-11+\dfrac{119}{3}-\dfrac{\dfrac{-\dfrac{5}{2}}{-1-\dfrac{44}{1875}+1+1}}{-\dfrac{125}{2}}\times\left(-\dfrac{125}{2}-\dfrac{105}{4}-\dfrac{1}{-1}\times\dfrac{105}{4}-\dfrac{43}{2}\right)+9\\&=&-11+\dfrac{119}{3}-\dfrac{\dfrac{-\dfrac{5}{2}}{-1-\dfrac{44}{1875}+1+1}}{-\dfrac{125}{2}}\times\left(-\dfrac{125}{2}-\dfrac{105}{4}-\left(-1\right)\times\dfrac{105}{4}-\dfrac{43}{2}\right)+9\\&=&-11+\dfrac{119}{3}-\dfrac{\dfrac{-\dfrac{5}{2}}{-\dfrac{1919}{1875}+1+1}}{-\dfrac{125}{2}}\times\left(-\dfrac{125}{2}-\dfrac{105}{4}-\left(-1\right)\times\dfrac{105}{4}-\dfrac{43}{2}\right)+9\\&=&-11+\dfrac{119}{3}-\dfrac{\dfrac{-\dfrac{5}{2}}{-\dfrac{44}{1875}+1}}{-\dfrac{125}{2}}\times\left(-\dfrac{125}{2}-\dfrac{105}{4}-\left(-1\right)\times\dfrac{105}{4}-\dfrac{43}{2}\right)+9\\&=&-11+\dfrac{119}{3}-\dfrac{\dfrac{-\dfrac{5}{2}}{\dfrac{1831}{1875}}}{-\dfrac{125}{2}}\times\left(-\dfrac{125}{2}-\dfrac{105}{4}-\left(-1\right)\times\dfrac{105}{4}-\dfrac{43}{2}\right)+9\\&=&-11+\dfrac{119}{3}-\dfrac{\dfrac{-\dfrac{5}{2}}{\dfrac{1831}{1875}}}{-\dfrac{125}{2}}\times\left(-\dfrac{125}{2}-\dfrac{105}{4}+\dfrac{105}{4}-\dfrac{43}{2}\right)+9\\&=&-11+\dfrac{119}{3}-\dfrac{-\dfrac{9375}{3662}}{-\dfrac{125}{2}}\times\left(-\dfrac{125}{2}-\dfrac{105}{4}+\dfrac{105}{4}-\dfrac{43}{2}\right)+9\\&=&-11+\dfrac{119}{3}-\dfrac{75}{1831}\times\left(-\dfrac{125}{2}-\dfrac{105}{4}+\dfrac{105}{4}-\dfrac{43}{2}\right)+9\\&=&-11+\dfrac{119}{3}-\dfrac{75}{1831}\times\left(-\dfrac{355}{4}+\dfrac{105}{4}-\dfrac{43}{2}\right)+9\\&=&-11+\dfrac{119}{3}-\dfrac{75}{1831}\times\left(-\dfrac{125}{2}-\dfrac{43}{2}\right)+9\\&=&-11+\dfrac{119}{3}-\dfrac{75}{1831}\times\left(-84\right)+9\\&=&-11+\dfrac{119}{3}+\dfrac{6300}{1831}+9\\&=&\dfrac{86}{3}+\dfrac{6300}{1831}+9\\&=&\dfrac{176366}{5493}+9\\&=&\dfrac{225803}{5493}\\
\end{eqnarray*}