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 \[\left(\dfrac{113}{3}-\left(\dfrac{29}{6}+\dfrac{\dfrac{25}{12}}{\dfrac{29}{6}}-\dfrac{69}{7}+\dfrac{93}{4}+\dfrac{\dfrac{\dfrac{-1}{\dfrac{69}{7}}}{-\dfrac{69}{7}}}{\dfrac{4}{3}+1+1}\right)\right)+1\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(\dfrac{113}{3}-\left(\dfrac{29}{6}+\dfrac{\dfrac{25}{12}}{\dfrac{29}{6}}-\dfrac{69}{7}+\dfrac{93}{4}+\dfrac{\dfrac{\dfrac{-1}{\dfrac{69}{7}}}{-\dfrac{69}{7}}}{\dfrac{4}{3}+1+1}\right)\right)+1=\dfrac{42968447}{2147740}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(\dfrac{113}{3}-\left(\dfrac{29}{6}+\dfrac{25}{58}-\dfrac{69}{7}+\dfrac{93}{4}+\dfrac{\dfrac{\dfrac{-1}{\dfrac{69}{7}}}{-\dfrac{69}{7}}}{\dfrac{4}{3}+1+1}\right)\right)+1\\&=&\left(\dfrac{113}{3}-\left(\dfrac{29}{6}+\dfrac{25}{58}-\dfrac{69}{7}+\dfrac{93}{4}+\dfrac{\dfrac{-\dfrac{7}{69}}{-\dfrac{69}{7}}}{\dfrac{4}{3}+1+1}\right)\right)+1\\&=&\left(\dfrac{113}{3}-\left(\dfrac{29}{6}+\dfrac{25}{58}-\dfrac{69}{7}+\dfrac{93}{4}+\dfrac{\dfrac{49}{4761}}{\dfrac{4}{3}+1+1}\right)\right)+1\\&=&\left(\dfrac{113}{3}-\left(\dfrac{29}{6}+\dfrac{25}{58}-\dfrac{69}{7}+\dfrac{93}{4}+\dfrac{\dfrac{49}{4761}}{\dfrac{7}{3}+1}\right)\right)+1\\&=&\left(\dfrac{113}{3}-\left(\dfrac{29}{6}+\dfrac{25}{58}-\dfrac{69}{7}+\dfrac{93}{4}+\dfrac{\dfrac{49}{4761}}{\dfrac{10}{3}}\right)\right)+1\\&=&\left(\dfrac{113}{3}-\left(\dfrac{458}{87}-\dfrac{69}{7}+\dfrac{93}{4}+\dfrac{\dfrac{49}{4761}}{\dfrac{10}{3}}\right)\right)+1\\&=&\left(\dfrac{113}{3}-\left(-\dfrac{2797}{609}+\dfrac{93}{4}+\dfrac{\dfrac{49}{4761}}{\dfrac{10}{3}}\right)\right)+1\\&=&\left(\dfrac{113}{3}-\left(-\dfrac{2797}{609}+\dfrac{93}{4}+\dfrac{49}{15870}\right)\right)+1\\&=&\left(\dfrac{113}{3}-\left(\dfrac{45449}{2436}+\dfrac{49}{15870}\right)\right)+1\\&=&\left(\dfrac{113}{3}-\dfrac{120232499}{6443220}\right)+1\\&=&\dfrac{40820707}{2147740}+1\\&=&\dfrac{42968447}{2147740}\\
\end{eqnarray*}