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 \[\dfrac{29}{5}-7-\left(-\dfrac{103}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{47}{4}}{\dfrac{112}{9}}}{\dfrac{24}{11}}}{\left(-\dfrac{73}{3}\right)\times\left(-\dfrac{47}{4}\right)\times\dfrac{135}{11}\times\dfrac{\dfrac{-\dfrac{103}{3}}{-\dfrac{73}{3}}}{10}\times\left(0-7+11-0\right)}\right)\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{29}{5}-7-\left(-\dfrac{103}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{47}{4}}{\dfrac{112}{9}}}{\dfrac{24}{11}}}{\left(-\dfrac{73}{3}\right)\times\left(-\dfrac{47}{4}\right)\times\dfrac{135}{11}\times\dfrac{\dfrac{-\dfrac{103}{3}}{-\dfrac{73}{3}}}{10}\times\left(0-7+11-0\right)}\right)=\dfrac{30577889}{922880}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{29}{5}-7-\left(-\dfrac{103}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{47}{4}}{\dfrac{112}{9}}}{\dfrac{24}{11}}}{\left(-\dfrac{73}{3}\right)\times\left(-\dfrac{6345}{44}\right)\times\dfrac{\dfrac{-\dfrac{103}{3}}{-\dfrac{73}{3}}}{10}\times\left(0-7+11-0\right)}\right)\\&=&\dfrac{29}{5}-7-\left(-\dfrac{103}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{47}{4}}{\dfrac{112}{9}}}{\dfrac{24}{11}}}{\left(-\dfrac{73}{3}\right)\times\left(-\dfrac{6345}{44}\right)\times\dfrac{\dfrac{103}{73}}{10}\times\left(0-7+11-0\right)}\right)\\&=&\dfrac{29}{5}-7-\left(-\dfrac{103}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{47}{4}}{\dfrac{112}{9}}}{\dfrac{24}{11}}}{\left(-\dfrac{73}{3}\right)\times\left(-\dfrac{6345}{44}\right)\times\dfrac{103}{730}\times\left(0-7+11-0\right)}\right)\\&=&\dfrac{29}{5}-7-\left(-\dfrac{103}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{47}{4}}{\dfrac{112}{9}}}{\dfrac{24}{11}}}{\left(-\dfrac{73}{3}\right)\times\left(-\dfrac{6345}{44}\right)\times\dfrac{103}{730}\times\left(-7+11-0\right)}\right)\\&=&\dfrac{29}{5}-7-\left(-\dfrac{103}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{47}{4}}{\dfrac{112}{9}}}{\dfrac{24}{11}}}{\left(-\dfrac{73}{3}\right)\times\left(-\dfrac{6345}{44}\right)\times\dfrac{103}{730}\times\left(4-0\right)}\right)\\&=&\dfrac{29}{5}-7-\left(-\dfrac{103}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{47}{4}}{\dfrac{112}{9}}}{\dfrac{24}{11}}}{\left(-\dfrac{73}{3}\right)\times\left(-\dfrac{6345}{44}\right)\times\dfrac{103}{730}\times4}\right)\\&=&\dfrac{29}{5}-7-\left(-\dfrac{103}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{47}{4}}{\dfrac{112}{9}}}{\dfrac{24}{11}}}{\dfrac{154395}{44}\times\dfrac{103}{730}\times4}\right)\\&=&\dfrac{29}{5}-7-\left(-\dfrac{103}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{47}{4}}{\dfrac{112}{9}}}{\dfrac{24}{11}}}{\dfrac{43569}{88}\times4}\right)\\&=&\dfrac{29}{5}-7-\left(-\dfrac{103}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{47}{4}}{\dfrac{112}{9}}}{\dfrac{24}{11}}}{\dfrac{43569}{22}}\right)\\&=&\dfrac{29}{5}-7-\left(-\dfrac{103}{3}-\dfrac{\dfrac{-\dfrac{423}{448}}{\dfrac{24}{11}}}{\dfrac{43569}{22}}\right)\\&=&\dfrac{29}{5}-7-\left(-\dfrac{103}{3}-\dfrac{-\dfrac{1551}{3584}}{\dfrac{43569}{22}}\right)\\&=&\dfrac{29}{5}-7-\left(-\dfrac{103}{3}+\dfrac{121}{553728}\right)\\&=&\dfrac{29}{5}-7+\dfrac{6337069}{184576}\\&=&-\dfrac{6}{5}+\dfrac{6337069}{184576}\\&=&\dfrac{30577889}{922880}\\
\end{eqnarray*}