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 \[4-5+5-4+\left(-12\right)\times\dfrac{\dfrac{8}{8}}{-\dfrac{83}{8}}\times\left(-5\right)\times\left(\dfrac{25}{9}+\left(-\dfrac{77}{12}\right)\times4-3+\dfrac{83}{8}+\dfrac{83}{8}+\dfrac{83}{8}-\dfrac{83}{8}\right)\times\left(-\dfrac{83}{8}\right)\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=4-5+5-4+\left(-12\right)\times\dfrac{\dfrac{8}{8}}{-\dfrac{83}{8}}\times\left(-5\right)\times\left(\dfrac{25}{9}+\left(-\dfrac{77}{12}\right)\times4-3+\dfrac{83}{8}+\dfrac{83}{8}+\dfrac{83}{8}-\dfrac{83}{8}\right)\times\left(-\dfrac{83}{8}\right)=-\dfrac{925}{3}\) . Voici le détail :
\begin{eqnarray*}
X &=&4-5+5-4+\left(-12\right)\times\dfrac{1}{-\dfrac{83}{8}}\times\left(-5\right)\times\left(\dfrac{25}{9}+\left(-\dfrac{77}{12}\right)\times4-3+\dfrac{83}{8}+\dfrac{83}{8}+\dfrac{83}{8}-\dfrac{83}{8}\right)\times\left(-\dfrac{83}{8}\right)\\&=&4-5+5-4+\left(-12\right)\times\left(-\dfrac{8}{83}\right)\times\left(-5\right)\times\left(\dfrac{25}{9}+\left(-\dfrac{77}{12}\right)\times4-3+\dfrac{83}{8}+\dfrac{83}{8}+\dfrac{83}{8}-\dfrac{83}{8}\right)\times\left(-\dfrac{83}{8}\right)\\&=&4-5+5-4+\left(-12\right)\times\left(-\dfrac{8}{83}\right)\times\left(-5\right)\times\left(\dfrac{25}{9}-\dfrac{77}{3}-3+\dfrac{83}{8}+\dfrac{83}{8}+\dfrac{83}{8}-\dfrac{83}{8}\right)\times\left(-\dfrac{83}{8}\right)\\&=&4-5+5-4+\left(-12\right)\times\left(-\dfrac{8}{83}\right)\times\left(-5\right)\times\left(\dfrac{25}{9}-\dfrac{77}{3}+\dfrac{59}{8}+\dfrac{83}{8}+\dfrac{83}{8}-\dfrac{83}{8}\right)\times\left(-\dfrac{83}{8}\right)\\&=&4-5+5-4+\left(-12\right)\times\left(-\dfrac{8}{83}\right)\times\left(-5\right)\times\left(\dfrac{25}{9}-\dfrac{77}{3}+\dfrac{71}{4}+\dfrac{83}{8}-\dfrac{83}{8}\right)\times\left(-\dfrac{83}{8}\right)\\&=&4-5+5-4+\left(-12\right)\times\left(-\dfrac{8}{83}\right)\times\left(-5\right)\times\left(\dfrac{25}{9}-\dfrac{77}{3}+\dfrac{225}{8}-\dfrac{83}{8}\right)\times\left(-\dfrac{83}{8}\right)\\&=&4-5+5-4+\left(-12\right)\times\dfrac{40}{83}\times\left(\dfrac{25}{9}-\dfrac{77}{3}+\dfrac{225}{8}-\dfrac{83}{8}\right)\times\left(-\dfrac{83}{8}\right)\\&=&4-5+5-4+\left(-12\right)\times\dfrac{40}{83}\times\left(-\dfrac{206}{9}+\dfrac{225}{8}-\dfrac{83}{8}\right)\times\left(-\dfrac{83}{8}\right)\\&=&4-5+5-4+\left(-12\right)\times\dfrac{40}{83}\times\left(\dfrac{377}{72}-\dfrac{83}{8}\right)\times\left(-\dfrac{83}{8}\right)\\&=&4-5+5-4+\left(-\dfrac{480}{83}\right)\times\left(\dfrac{377}{72}-\dfrac{83}{8}\right)\times\left(-\dfrac{83}{8}\right)\\&=&4-5+5-4+\left(-\dfrac{480}{83}\right)\times\left(-\dfrac{185}{36}\right)\times\left(-\dfrac{83}{8}\right)\\&=&4+0-4+\left(-\dfrac{480}{83}\right)\times\left(-\dfrac{185}{36}\right)\times\left(-\dfrac{83}{8}\right)\\&=&4-4+\left(-\dfrac{480}{83}\right)\times\left(-\dfrac{185}{36}\right)\times\left(-\dfrac{83}{8}\right)\\&=&4-4+\dfrac{7400}{249}\times\left(-\dfrac{83}{8}\right)\\&=&4-4-\dfrac{925}{3}\\&=&0-\dfrac{925}{3}\\&=&-\dfrac{925}{3}\\
\end{eqnarray*}