L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\left(-11\right)\times\left(-3\right)\times\left(-\dfrac{122}{5}\right)\times\left(-\dfrac{67}{5}+\dfrac{45}{4}\times0\times\left(-\dfrac{122}{5}\right)+\dfrac{15}{8}\right)\times\left(-\dfrac{67}{5}\right)\times\left(4+\dfrac{\dfrac{45}{4}}{-9}+\dfrac{15}{8}\times\dfrac{58}{3}\times\dfrac{3}{2}\right)\times\left(-\dfrac{29}{7}\right)\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\left(-11\right)\times\left(-3\right)\times\left(-\dfrac{122}{5}\right)\times\left(-\dfrac{67}{5}+\dfrac{45}{4}\times0\times\left(-\dfrac{122}{5}\right)+\dfrac{15}{8}\right)\times\left(-\dfrac{67}{5}\right)\times\left(4+\dfrac{\dfrac{45}{4}}{-9}+\dfrac{15}{8}\times\dfrac{58}{3}\times\dfrac{3}{2}\right)\times\left(-\dfrac{29}{7}\right)=-\dfrac{71689071173841}{392000}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\left(-11\right)\times\left(-3\right)\times\left(-\dfrac{122}{5}\right)\times\left(-\dfrac{67}{5}+0\times\left(-\dfrac{122}{5}\right)+\dfrac{15}{8}\right)\times\left(-\dfrac{67}{5}\right)\times\left(4+\dfrac{\dfrac{45}{4}}{-9}+\dfrac{15}{8}\times\dfrac{58}{3}\times\dfrac{3}{2}\right)\times\left(-\dfrac{29}{7}\right)\\&=&\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\left(-11\right)\times\left(-3\right)\times\left(-\dfrac{122}{5}\right)\times\left(-\dfrac{67}{5}+0+\dfrac{15}{8}\right)\times\left(-\dfrac{67}{5}\right)\times\left(4+\dfrac{\dfrac{45}{4}}{-9}+\dfrac{15}{8}\times\dfrac{58}{3}\times\dfrac{3}{2}\right)\times\left(-\dfrac{29}{7}\right)\\&=&\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times33\times\left(-\dfrac{122}{5}\right)\times\left(-\dfrac{67}{5}+0+\dfrac{15}{8}\right)\times\left(-\dfrac{67}{5}\right)\times\left(4+\dfrac{\dfrac{45}{4}}{-9}+\dfrac{15}{8}\times\dfrac{58}{3}\times\dfrac{3}{2}\right)\times\left(-\dfrac{29}{7}\right)\\&=&\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\left(-\dfrac{4026}{5}\right)\times\left(-\dfrac{67}{5}+0+\dfrac{15}{8}\right)\times\left(-\dfrac{67}{5}\right)\times\left(4+\dfrac{\dfrac{45}{4}}{-9}+\dfrac{15}{8}\times\dfrac{58}{3}\times\dfrac{3}{2}\right)\times\left(-\dfrac{29}{7}\right)\\&=&\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\left(-\dfrac{4026}{5}\right)\times\left(-\dfrac{67}{5}+\dfrac{15}{8}\right)\times\left(-\dfrac{67}{5}\right)\times\left(4+\dfrac{\dfrac{45}{4}}{-9}+\dfrac{15}{8}\times\dfrac{58}{3}\times\dfrac{3}{2}\right)\times\left(-\dfrac{29}{7}\right)\\&=&\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\left(-\dfrac{4026}{5}\right)\times-\dfrac{461}{40}\times\left(-\dfrac{67}{5}\right)\times\left(4+\dfrac{\dfrac{45}{4}}{-9}+\dfrac{15}{8}\times\dfrac{58}{3}\times\dfrac{3}{2}\right)\times\left(-\dfrac{29}{7}\right)\\&=&\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\left(-\dfrac{4026}{5}\right)\times-\dfrac{461}{40}\times\left(-\dfrac{67}{5}\right)\times\left(4-\dfrac{5}{4}+\dfrac{15}{8}\times\dfrac{58}{3}\times\dfrac{3}{2}\right)\times\left(-\dfrac{29}{7}\right)\\&=&\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\left(-\dfrac{4026}{5}\right)\times-\dfrac{461}{40}\times\left(-\dfrac{67}{5}\right)\times\left(4-\dfrac{5}{4}+\dfrac{145}{4}\times\dfrac{3}{2}\right)\times\left(-\dfrac{29}{7}\right)\\&=&\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\left(-\dfrac{4026}{5}\right)\times-\dfrac{461}{40}\times\left(-\dfrac{67}{5}\right)\times\left(4-\dfrac{5}{4}+\dfrac{435}{8}\right)\times\left(-\dfrac{29}{7}\right)\\&=&\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\dfrac{927993}{100}\times\left(-\dfrac{67}{5}\right)\times\left(4-\dfrac{5}{4}+\dfrac{435}{8}\right)\times\left(-\dfrac{29}{7}\right)\\&=&\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\left(-\dfrac{62175531}{500}\right)\times\left(4-\dfrac{5}{4}+\dfrac{435}{8}\right)\times\left(-\dfrac{29}{7}\right)\\&=&\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\left(-\dfrac{62175531}{500}\right)\times\left(\dfrac{11}{4}+\dfrac{435}{8}\right)\times\left(-\dfrac{29}{7}\right)\\&=&\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\left(-\dfrac{62175531}{500}\right)\times\dfrac{457}{8}\times\left(-\dfrac{29}{7}\right)\\&=&\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\left(-\dfrac{28414217667}{4000}\right)\times\left(-\dfrac{29}{7}\right)\\&=&\left(-\dfrac{29}{7}\right)\times\dfrac{3}{2}\times\dfrac{824012312343}{28000}\\&=&\left(-\dfrac{87}{14}\right)\times\dfrac{824012312343}{28000}\\&=&-\dfrac{71689071173841}{392000}\\
\end{eqnarray*}