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 \[\dfrac{\dfrac{\dfrac{\dfrac{57}{4}+1}{\dfrac{5+1}{10}-\left(\dfrac{23}{8}-\dfrac{23}{8}\right)+\dfrac{102}{7}}}{-4}}{10\times\dfrac{107}{4}\times1}\times\dfrac{23}{8}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{\dfrac{57}{4}+1}{\dfrac{5+1}{10}-\left(\dfrac{23}{8}-\dfrac{23}{8}\right)+\dfrac{102}{7}}}{-4}}{10\times\dfrac{107}{4}\times1}\times\dfrac{23}{8}=-\dfrac{9821}{3636288}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{\dfrac{57}{4}+1}{\dfrac{6}{10}-\left(\dfrac{23}{8}-\dfrac{23}{8}\right)+\dfrac{102}{7}}}{-4}}{10\times\dfrac{107}{4}\times1}\times\dfrac{23}{8}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{57}{4}+1}{\dfrac{3}{5}-\left(\dfrac{23}{8}-\dfrac{23}{8}\right)+\dfrac{102}{7}}}{-4}}{10\times\dfrac{107}{4}\times1}\times\dfrac{23}{8}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{57}{4}+1}{\dfrac{3}{5}-0+\dfrac{102}{7}}}{-4}}{10\times\dfrac{107}{4}\times1}\times\dfrac{23}{8}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{61}{4}}{\dfrac{3}{5}-0+\dfrac{102}{7}}}{-4}}{10\times\dfrac{107}{4}\times1}\times\dfrac{23}{8}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{61}{4}}{\dfrac{3}{5}+\dfrac{102}{7}}}{-4}}{10\times\dfrac{107}{4}\times1}\times\dfrac{23}{8}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{61}{4}}{\dfrac{531}{35}}}{-4}}{10\times\dfrac{107}{4}\times1}\times\dfrac{23}{8}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{61}{4}}{\dfrac{531}{35}}}{-4}}{\dfrac{535}{2}\times1}\times\dfrac{23}{8}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{61}{4}}{\dfrac{531}{35}}}{-4}}{\dfrac{535}{2}}\times\dfrac{23}{8}\\&=&\dfrac{\dfrac{\dfrac{2135}{2124}}{-4}}{\dfrac{535}{2}}\times\dfrac{23}{8}\\&=&\dfrac{-\dfrac{2135}{8496}}{\dfrac{535}{2}}\times\dfrac{23}{8}\\&=&\left(-\dfrac{427}{454536}\right)\times\dfrac{23}{8}\\&=&-\dfrac{9821}{3636288}\\
\end{eqnarray*}