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 \[\dfrac{96}{7}\times\dfrac{3}{4}\times\dfrac{7}{5}\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{3}{4}-\dfrac{96}{7}}{\dfrac{7}{5}+7-\dfrac{27}{4}}}{5+4}}{5}}{-\dfrac{110}{9}}\times7\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{96}{7}\times\dfrac{3}{4}\times\dfrac{7}{5}\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{3}{4}-\dfrac{96}{7}}{\dfrac{7}{5}+7-\dfrac{27}{4}}}{5+4}}{5}}{-\dfrac{110}{9}}\times7=\dfrac{36}{25}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{96}{7}\times\dfrac{3}{4}\times\dfrac{7}{5}\times\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{363}{28}}{\dfrac{7}{5}+7-\dfrac{27}{4}}}{5+4}}{5}}{-\dfrac{110}{9}}\times7\\&=&\dfrac{96}{7}\times\dfrac{3}{4}\times\dfrac{7}{5}\times\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{363}{28}}{\dfrac{42}{5}-\dfrac{27}{4}}}{5+4}}{5}}{-\dfrac{110}{9}}\times7\\&=&\dfrac{96}{7}\times\dfrac{3}{4}\times\dfrac{7}{5}\times\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{363}{28}}{\dfrac{33}{20}}}{5+4}}{5}}{-\dfrac{110}{9}}\times7\\&=&\dfrac{96}{7}\times\dfrac{3}{4}\times\dfrac{7}{5}\times\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{363}{28}}{\dfrac{33}{20}}}{9}}{5}}{-\dfrac{110}{9}}\times7\\&=&\dfrac{96}{7}\times\dfrac{3}{4}\times\dfrac{7}{5}\times\dfrac{\dfrac{\dfrac{-\dfrac{55}{7}}{9}}{5}}{-\dfrac{110}{9}}\times7\\&=&\dfrac{96}{7}\times\dfrac{3}{4}\times\dfrac{7}{5}\times\dfrac{\dfrac{-\dfrac{55}{63}}{5}}{-\dfrac{110}{9}}\times7\\&=&\dfrac{72}{7}\times\dfrac{7}{5}\times\dfrac{\dfrac{-\dfrac{55}{63}}{5}}{-\dfrac{110}{9}}\times7\\&=&\dfrac{72}{5}\times\dfrac{\dfrac{-\dfrac{55}{63}}{5}}{-\dfrac{110}{9}}\times7\\&=&\dfrac{72}{5}\times\dfrac{-\dfrac{11}{63}}{-\dfrac{110}{9}}\times7\\&=&\dfrac{72}{5}\times\dfrac{1}{70}\times7\\&=&\dfrac{36}{175}\times7\\&=&\dfrac{36}{25}\\
\end{eqnarray*}