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 \[\left(-\dfrac{107}{6}\right)\times\dfrac{\dfrac{1}{6}}{\dfrac{124}{7}}\times\left(-\dfrac{7}{4}-11\times\left(-7\right)\times\left(-\dfrac{107}{6}\right)\times8+3-\dfrac{83}{6}\right)\times\left(\dfrac{22}{9}-\left(-4-8+7\right)\right)\times\left(-2\right)+11\times\left(-3\right)-2+\dfrac{124}{7}+\dfrac{124}{7}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(-\dfrac{107}{6}\right)\times\dfrac{\dfrac{1}{6}}{\dfrac{124}{7}}\times\left(-\dfrac{7}{4}-11\times\left(-7\right)\times\left(-\dfrac{107}{6}\right)\times8+3-\dfrac{83}{6}\right)\times\left(\dfrac{22}{9}-\left(-4-8+7\right)\right)\times\left(-2\right)+11\times\left(-3\right)-2+\dfrac{124}{7}+\dfrac{124}{7}=-\dfrac{649034215298}{23623488}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-\dfrac{107}{6}\right)\times\dfrac{\dfrac{1}{6}}{\dfrac{124}{7}}\times\left(-\dfrac{7}{4}-\left(-77\right)\times\left(-\dfrac{107}{6}\right)\times8+3-\dfrac{83}{6}\right)\times\left(\dfrac{22}{9}-\left(-4-8+7\right)\right)\times\left(-2\right)+11\times\left(-3\right)-2+\dfrac{124}{7}+\dfrac{124}{7}\\&=&\left(-\dfrac{107}{6}\right)\times\dfrac{\dfrac{1}{6}}{\dfrac{124}{7}}\times\left(-\dfrac{7}{4}-\dfrac{8239}{6}\times8+3-\dfrac{83}{6}\right)\times\left(\dfrac{22}{9}-\left(-4-8+7\right)\right)\times\left(-2\right)+11\times\left(-3\right)-2+\dfrac{124}{7}+\dfrac{124}{7}\\&=&\left(-\dfrac{107}{6}\right)\times\dfrac{\dfrac{1}{6}}{\dfrac{124}{7}}\times\left(-\dfrac{7}{4}-\dfrac{32956}{3}+3-\dfrac{83}{6}\right)\times\left(\dfrac{22}{9}-\left(-4-8+7\right)\right)\times\left(-2\right)+11\times\left(-3\right)-2+\dfrac{124}{7}+\dfrac{124}{7}\\&=&\left(-\dfrac{107}{6}\right)\times\dfrac{\dfrac{1}{6}}{\dfrac{124}{7}}\times\left(-\dfrac{7}{4}-\dfrac{32956}{3}+3-\dfrac{83}{6}\right)\times\left(\dfrac{22}{9}-\left(-12+7\right)\right)\times\left(-2\right)+11\times\left(-3\right)-2+\dfrac{124}{7}+\dfrac{124}{7}\\&=&\left(-\dfrac{107}{6}\right)\times\dfrac{\dfrac{1}{6}}{\dfrac{124}{7}}\times\left(-\dfrac{7}{4}-\dfrac{32956}{3}+3-\dfrac{83}{6}\right)\times\left(\dfrac{22}{9}+5\right)\times\left(-2\right)+11\times\left(-3\right)-2+\dfrac{124}{7}+\dfrac{124}{7}\\&=&\left(-\dfrac{107}{6}\right)\times\dfrac{7}{744}\times\left(-\dfrac{7}{4}-\dfrac{32956}{3}+3-\dfrac{83}{6}\right)\times\left(\dfrac{22}{9}+5\right)\times\left(-2\right)+11\times\left(-3\right)-2+\dfrac{124}{7}+\dfrac{124}{7}\\&=&\left(-\dfrac{107}{6}\right)\times\dfrac{7}{744}\times\left(-\dfrac{131845}{12}+3-\dfrac{83}{6}\right)\times\left(\dfrac{22}{9}+5\right)\times\left(-2\right)+11\times\left(-3\right)-2+\dfrac{124}{7}+\dfrac{124}{7}\\&=&\left(-\dfrac{107}{6}\right)\times\dfrac{7}{744}\times\left(-\dfrac{131809}{12}-\dfrac{83}{6}\right)\times\left(\dfrac{22}{9}+5\right)\times\left(-2\right)+11\times\left(-3\right)-2+\dfrac{124}{7}+\dfrac{124}{7}\\&=&\left(-\dfrac{107}{6}\right)\times\dfrac{7}{744}\times\left(-\dfrac{131975}{12}\right)\times\left(\dfrac{22}{9}+5\right)\times\left(-2\right)+11\times\left(-3\right)-2+\dfrac{124}{7}+\dfrac{124}{7}\\&=&\left(-\dfrac{107}{6}\right)\times\dfrac{7}{744}\times\left(-\dfrac{131975}{12}\right)\times\dfrac{67}{9}\times\left(-2\right)+11\times\left(-3\right)-2+\dfrac{124}{7}+\dfrac{124}{7}\\&=&\left(-\dfrac{107}{6}\right)\times\left(-\dfrac{923825}{8928}\right)\times\dfrac{67}{9}\times\left(-2\right)+11\times\left(-3\right)-2+\dfrac{124}{7}+\dfrac{124}{7}\\&=&\left(-\dfrac{107}{6}\right)\times\left(-\dfrac{61896275}{80352}\right)\times\left(-2\right)+11\times\left(-3\right)-2+\dfrac{124}{7}+\dfrac{124}{7}\\&=&\left(-\dfrac{107}{6}\right)\times\left(-\dfrac{61896275}{80352}\right)\times\left(-2\right)-33-2+\dfrac{124}{7}+\dfrac{124}{7}\\&=&\dfrac{6622901425}{482112}\times\left(-2\right)-33-2+\dfrac{124}{7}+\dfrac{124}{7}\\&=&-\dfrac{13245802850}{482112}-33-2+\dfrac{124}{7}+\dfrac{124}{7}\\&=&-\dfrac{13245802850}{482112}-35+\dfrac{124}{7}+\dfrac{124}{7}\\&=&-\dfrac{13245802850}{482112}-\dfrac{121}{7}+\dfrac{124}{7}\\&=&-\dfrac{92778955502}{3374784}+\dfrac{124}{7}\\&=&-\dfrac{649034215298}{23623488}\\
\end{eqnarray*}