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 \[-\dfrac{13}{6}+\dfrac{\left(0-\dfrac{121}{2}\right)-\left(-\dfrac{13}{6}\right)\times\left(-12\right)\times\dfrac{141}{7}-\dfrac{63}{2}-\left(0+\dfrac{67}{6}\right)+\dfrac{25}{12}+0\times\left(-\dfrac{23}{2}+\dfrac{121}{2}\right)\times\dfrac{\dfrac{\dfrac{23}{2}}{-\dfrac{23}{2}}}{0}}{\dfrac{0+12+\dfrac{23}{2}+0+\dfrac{134}{7}-7-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=-\dfrac{13}{6}+\dfrac{\left(0-\dfrac{121}{2}\right)-\left(-\dfrac{13}{6}\right)\times\left(-12\right)\times\dfrac{141}{7}-\dfrac{63}{2}-\left(0+\dfrac{67}{6}\right)+\dfrac{25}{12}+0\times\left(-\dfrac{23}{2}+\dfrac{121}{2}\right)\times\dfrac{\dfrac{\dfrac{23}{2}}{-\dfrac{23}{2}}}{0}}{\dfrac{0+12+\dfrac{23}{2}+0+\dfrac{134}{7}-7-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}=\dfrac{1096397}{1352}\) . Voici le détail :
\begin{eqnarray*}
X &=&-\dfrac{13}{6}+\dfrac{-\dfrac{121}{2}-\left(-\dfrac{13}{6}\right)\times\left(-12\right)\times\dfrac{141}{7}-\dfrac{63}{2}-\left(0+\dfrac{67}{6}\right)+\dfrac{25}{12}+0\times\left(-\dfrac{23}{2}+\dfrac{121}{2}\right)\times\dfrac{\dfrac{\dfrac{23}{2}}{-\dfrac{23}{2}}}{0}}{\dfrac{0+12+\dfrac{23}{2}+0+\dfrac{134}{7}-7-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{121}{2}-26\times\dfrac{141}{7}-\dfrac{63}{2}-\left(0+\dfrac{67}{6}\right)+\dfrac{25}{12}+0\times\left(-\dfrac{23}{2}+\dfrac{121}{2}\right)\times\dfrac{\dfrac{\dfrac{23}{2}}{-\dfrac{23}{2}}}{0}}{\dfrac{0+12+\dfrac{23}{2}+0+\dfrac{134}{7}-7-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{121}{2}-\dfrac{3666}{7}-\dfrac{63}{2}-\left(0+\dfrac{67}{6}\right)+\dfrac{25}{12}+0\times\left(-\dfrac{23}{2}+\dfrac{121}{2}\right)\times\dfrac{\dfrac{\dfrac{23}{2}}{-\dfrac{23}{2}}}{0}}{\dfrac{0+12+\dfrac{23}{2}+0+\dfrac{134}{7}-7-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{121}{2}-\dfrac{3666}{7}-\dfrac{63}{2}-\dfrac{67}{6}+\dfrac{25}{12}+0\times\left(-\dfrac{23}{2}+\dfrac{121}{2}\right)\times\dfrac{\dfrac{\dfrac{23}{2}}{-\dfrac{23}{2}}}{0}}{\dfrac{0+12+\dfrac{23}{2}+0+\dfrac{134}{7}-7-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{121}{2}-\dfrac{3666}{7}-\dfrac{63}{2}-\dfrac{67}{6}+\dfrac{25}{12}+0\times49\times\dfrac{\dfrac{\dfrac{23}{2}}{-\dfrac{23}{2}}}{0}}{\dfrac{0+12+\dfrac{23}{2}+0+\dfrac{134}{7}-7-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{121}{2}-\dfrac{3666}{7}-\dfrac{63}{2}-\dfrac{67}{6}+\dfrac{25}{12}+0\times49\times\dfrac{-1}{0}}{\dfrac{0+12+\dfrac{23}{2}+0+\dfrac{134}{7}-7-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{121}{2}-\dfrac{3666}{7}-\dfrac{63}{2}-\dfrac{67}{6}+\dfrac{25}{12}+0\times49\times0}{\dfrac{0+12+\dfrac{23}{2}+0+\dfrac{134}{7}-7-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{121}{2}-\dfrac{3666}{7}-\dfrac{63}{2}-\dfrac{67}{6}+\dfrac{25}{12}+0\times49\times0}{\dfrac{12+\dfrac{23}{2}+0+\dfrac{134}{7}-7-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{121}{2}-\dfrac{3666}{7}-\dfrac{63}{2}-\dfrac{67}{6}+\dfrac{25}{12}+0\times49\times0}{\dfrac{\dfrac{47}{2}+0+\dfrac{134}{7}-7-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{121}{2}-\dfrac{3666}{7}-\dfrac{63}{2}-\dfrac{67}{6}+\dfrac{25}{12}+0\times49\times0}{\dfrac{\dfrac{47}{2}+\dfrac{134}{7}-7-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{121}{2}-\dfrac{3666}{7}-\dfrac{63}{2}-\dfrac{67}{6}+\dfrac{25}{12}+0\times49\times0}{\dfrac{\dfrac{47}{2}+\dfrac{85}{7}-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{8179}{14}-\dfrac{63}{2}-\dfrac{67}{6}+\dfrac{25}{12}+0\times49\times0}{\dfrac{\dfrac{47}{2}+\dfrac{85}{7}-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{8179}{14}-\dfrac{128}{3}+\dfrac{25}{12}+0\times49\times0}{\dfrac{\dfrac{47}{2}+\dfrac{85}{7}-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{8179}{14}-\dfrac{487}{12}+0\times49\times0}{\dfrac{\dfrac{47}{2}+\dfrac{85}{7}-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{8179}{14}-\dfrac{487}{12}+0\times0}{\dfrac{\dfrac{47}{2}+\dfrac{85}{7}-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{8179}{14}-\dfrac{487}{12}+0}{\dfrac{\dfrac{47}{2}+\dfrac{85}{7}-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{8179}{14}-\dfrac{487}{12}+0}{\dfrac{\dfrac{499}{14}-\dfrac{23}{2}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{8179}{14}-\dfrac{487}{12}+0}{\dfrac{\dfrac{169}{7}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{52483}{84}+0}{\dfrac{\dfrac{169}{7}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{52483}{84}}{\dfrac{\dfrac{169}{7}}{-\dfrac{63}{2}}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{-\dfrac{52483}{84}}{-\dfrac{338}{441}}-\dfrac{25}{12}\\&=&-\dfrac{13}{6}+\dfrac{1102143}{1352}-\dfrac{25}{12}\\&=&\dfrac{3297641}{4056}-\dfrac{25}{12}\\&=&\dfrac{1096397}{1352}\\
\end{eqnarray*}