L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(\left(-\dfrac{22}{5}\right)\times\left(-12-\dfrac{61}{4}\right)\times\dfrac{\dfrac{96}{5}}{\dfrac{31}{3}}-\dfrac{33}{4}-\dfrac{33}{4}+\left(-\dfrac{22}{5}\right)\times\left(-\dfrac{33}{4}\right)\times\dfrac{31}{3}-3-\dfrac{131}{3}-12\right)-9+10\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(\left(-\dfrac{22}{5}\right)\times\left(-12-\dfrac{61}{4}\right)\times\dfrac{\dfrac{96}{5}}{\dfrac{31}{3}}-\dfrac{33}{4}-\dfrac{33}{4}+\left(-\dfrac{22}{5}\right)\times\left(-\dfrac{33}{4}\right)\times\dfrac{31}{3}-3-\dfrac{131}{3}-12\right)-9+10=\dfrac{1217638}{2325}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(\left(-\dfrac{22}{5}\right)\times-\dfrac{109}{4}\times\dfrac{\dfrac{96}{5}}{\dfrac{31}{3}}-\dfrac{33}{4}-\dfrac{33}{4}+\left(-\dfrac{22}{5}\right)\times\left(-\dfrac{33}{4}\right)\times\dfrac{31}{3}-3-\dfrac{131}{3}-12\right)-9+10\\&=&\left(\left(-\dfrac{22}{5}\right)\times-\dfrac{109}{4}\times\dfrac{288}{155}-\dfrac{33}{4}-\dfrac{33}{4}+\left(-\dfrac{22}{5}\right)\times\left(-\dfrac{33}{4}\right)\times\dfrac{31}{3}-3-\dfrac{131}{3}-12\right)-9+10\\&=&\left(\left(-\dfrac{22}{5}\right)\times-\dfrac{109}{4}\times\dfrac{288}{155}-\dfrac{33}{4}-\dfrac{33}{4}+\dfrac{363}{10}\times\dfrac{31}{3}-3-\dfrac{131}{3}-12\right)-9+10\\&=&\left(\left(-\dfrac{22}{5}\right)\times-\dfrac{109}{4}\times\dfrac{288}{155}-\dfrac{33}{4}-\dfrac{33}{4}+\dfrac{3751}{10}-3-\dfrac{131}{3}-12\right)-9+10\\&=&\left(\dfrac{1199}{10}\times\dfrac{288}{155}-\dfrac{33}{4}-\dfrac{33}{4}+\dfrac{3751}{10}-3-\dfrac{131}{3}-12\right)-9+10\\&=&\left(\dfrac{172656}{775}-\dfrac{33}{4}-\dfrac{33}{4}+\dfrac{3751}{10}-3-\dfrac{131}{3}-12\right)-9+10\\&=&\left(\dfrac{172656}{775}-\dfrac{33}{4}+\dfrac{7337}{20}-3-\dfrac{131}{3}-12\right)-9+10\\&=&\left(\dfrac{172656}{775}-\dfrac{33}{4}+\dfrac{7277}{20}-\dfrac{131}{3}-12\right)-9+10\\&=&\left(\dfrac{172656}{775}-\dfrac{33}{4}+\dfrac{19211}{60}-12\right)-9+10\\&=&\left(\dfrac{665049}{3100}+\dfrac{19211}{60}-12\right)-9+10\\&=&\left(\dfrac{1243213}{2325}-12\right)-9+10\\&=&\dfrac{1215313}{2325}-9+10\\&=&\dfrac{1194388}{2325}+10\\&=&\dfrac{1217638}{2325}\\
\end{eqnarray*}