L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{\dfrac{\dfrac{-\dfrac{37}{12}+\dfrac{29}{7}-0}{8}}{-\dfrac{29}{7}}}{\dfrac{\dfrac{\dfrac{59}{8}}{0}}{\dfrac{59}{8}}-0-\left(-\dfrac{37}{12}+\dfrac{25}{2}+2-\dfrac{59}{8}\right)-\left(-2\right)\times\left(-\dfrac{29}{7}\right)\times\dfrac{144}{5}}\times\dfrac{144}{5}+0\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{\dfrac{\dfrac{-\dfrac{37}{12}+\dfrac{29}{7}-0}{8}}{-\dfrac{29}{7}}}{\dfrac{\dfrac{\dfrac{59}{8}}{0}}{\dfrac{59}{8}}-0-\left(-\dfrac{37}{12}+\dfrac{25}{2}+2-\dfrac{59}{8}\right)-\left(-2\right)\times\left(-\dfrac{29}{7}\right)\times\dfrac{144}{5}}\times\dfrac{144}{5}+0=\dfrac{3841672591}{520207336}\) . Voici le détail :
\begin{eqnarray*}
X &=&0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{\dfrac{\dfrac{-\dfrac{37}{12}+\dfrac{29}{7}-0}{8}}{-\dfrac{29}{7}}}{\dfrac{0}{\dfrac{59}{8}}-0-\left(-\dfrac{37}{12}+\dfrac{25}{2}+2-\dfrac{59}{8}\right)-\left(-2\right)\times\left(-\dfrac{29}{7}\right)\times\dfrac{144}{5}}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{\dfrac{\dfrac{-\dfrac{37}{12}+\dfrac{29}{7}-0}{8}}{-\dfrac{29}{7}}}{0-0-\left(-\dfrac{37}{12}+\dfrac{25}{2}+2-\dfrac{59}{8}\right)-\left(-2\right)\times\left(-\dfrac{29}{7}\right)\times\dfrac{144}{5}}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{\dfrac{\dfrac{-\dfrac{37}{12}+\dfrac{29}{7}-0}{8}}{-\dfrac{29}{7}}}{0-0-\left(\dfrac{113}{12}+2-\dfrac{59}{8}\right)-\left(-2\right)\times\left(-\dfrac{29}{7}\right)\times\dfrac{144}{5}}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{\dfrac{\dfrac{-\dfrac{37}{12}+\dfrac{29}{7}-0}{8}}{-\dfrac{29}{7}}}{0-0-\left(\dfrac{137}{12}-\dfrac{59}{8}\right)-\left(-2\right)\times\left(-\dfrac{29}{7}\right)\times\dfrac{144}{5}}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{\dfrac{\dfrac{-\dfrac{37}{12}+\dfrac{29}{7}-0}{8}}{-\dfrac{29}{7}}}{0-0-\dfrac{97}{24}-\left(-2\right)\times\left(-\dfrac{29}{7}\right)\times\dfrac{144}{5}}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{\dfrac{\dfrac{-\dfrac{37}{12}+\dfrac{29}{7}-0}{8}}{-\dfrac{29}{7}}}{0-0-\dfrac{97}{24}-\dfrac{58}{7}\times\dfrac{144}{5}}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{\dfrac{\dfrac{-\dfrac{37}{12}+\dfrac{29}{7}-0}{8}}{-\dfrac{29}{7}}}{0-0-\dfrac{97}{24}-\dfrac{8352}{35}}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{\dfrac{\dfrac{\dfrac{89}{84}-0}{8}}{-\dfrac{29}{7}}}{0-0-\dfrac{97}{24}-\dfrac{8352}{35}}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{\dfrac{\dfrac{\dfrac{89}{84}}{8}}{-\dfrac{29}{7}}}{0-0-\dfrac{97}{24}-\dfrac{8352}{35}}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{\dfrac{\dfrac{\dfrac{89}{84}}{8}}{-\dfrac{29}{7}}}{0-\dfrac{97}{24}-\dfrac{8352}{35}}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{\dfrac{\dfrac{\dfrac{89}{84}}{8}}{-\dfrac{29}{7}}}{-\dfrac{97}{24}-\dfrac{8352}{35}}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{\dfrac{\dfrac{\dfrac{89}{84}}{8}}{-\dfrac{29}{7}}}{-\dfrac{203843}{840}}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{\dfrac{\dfrac{89}{672}}{-\dfrac{29}{7}}}{-\dfrac{203843}{840}}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{-\dfrac{89}{2784}}{-\dfrac{203843}{840}}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{43}{6}\times\dfrac{4}{11}\times\dfrac{3115}{23645788}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{86}{33}\times\dfrac{3115}{23645788}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{133945}{390155502}\times\dfrac{144}{5}+0\\&=&0+\dfrac{59}{8}+\dfrac{642936}{65025917}+0\\&=&\dfrac{59}{8}+\dfrac{642936}{65025917}+0\\&=&\dfrac{3841672591}{520207336}+0\\&=&\dfrac{3841672591}{520207336}\\
\end{eqnarray*}