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 \[\left(-9+\dfrac{81}{8}-\dfrac{8}{3}+\left(-7\right)\times\left(-\dfrac{87}{4}\right)\right)\times\dfrac{31}{8}\times\left(0-\left(\dfrac{-\dfrac{40}{3}}{2}-9\right)\right)\times\left(\dfrac{9-\dfrac{40}{3}}{\dfrac{\dfrac{81}{8}}{9}}-\dfrac{-9}{\dfrac{125}{3}}\right)\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(-9+\dfrac{81}{8}-\dfrac{8}{3}+\left(-7\right)\times\left(-\dfrac{87}{4}\right)\right)\times\dfrac{31}{8}\times\left(0-\left(\dfrac{-\dfrac{40}{3}}{2}-9\right)\right)\times\left(\dfrac{9-\dfrac{40}{3}}{\dfrac{\dfrac{81}{8}}{9}}-\dfrac{-9}{\dfrac{125}{3}}\right)=-\dfrac{64667789599}{1944000}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-9+\dfrac{179}{24}+\left(-7\right)\times\left(-\dfrac{87}{4}\right)\right)\times\dfrac{31}{8}\times\left(0-\left(\dfrac{-\dfrac{40}{3}}{2}-9\right)\right)\times\left(\dfrac{9-\dfrac{40}{3}}{\dfrac{\dfrac{81}{8}}{9}}-\dfrac{-9}{\dfrac{125}{3}}\right)\\&=&\left(-9+\dfrac{179}{24}+\dfrac{609}{4}\right)\times\dfrac{31}{8}\times\left(0-\left(\dfrac{-\dfrac{40}{3}}{2}-9\right)\right)\times\left(\dfrac{9-\dfrac{40}{3}}{\dfrac{\dfrac{81}{8}}{9}}-\dfrac{-9}{\dfrac{125}{3}}\right)\\&=&\left(-9+\dfrac{179}{24}+\dfrac{609}{4}\right)\times\dfrac{31}{8}\times\left(0-\left(-\dfrac{20}{3}-9\right)\right)\times\left(\dfrac{9-\dfrac{40}{3}}{\dfrac{\dfrac{81}{8}}{9}}-\dfrac{-9}{\dfrac{125}{3}}\right)\\&=&\left(-9+\dfrac{179}{24}+\dfrac{609}{4}\right)\times\dfrac{31}{8}\times\left(0-\left(-\dfrac{20}{3}-9\right)\right)\times\left(\dfrac{-\dfrac{13}{3}}{\dfrac{\dfrac{81}{8}}{9}}-\dfrac{-9}{\dfrac{125}{3}}\right)\\&=&\left(-9+\dfrac{179}{24}+\dfrac{609}{4}\right)\times\dfrac{31}{8}\times\left(0-\left(-\dfrac{20}{3}-9\right)\right)\times\left(\dfrac{-\dfrac{13}{3}}{\dfrac{9}{8}}-\dfrac{-9}{\dfrac{125}{3}}\right)\\&=&\left(-9+\dfrac{3833}{24}\right)\times\dfrac{31}{8}\times\left(0-\left(-\dfrac{20}{3}-9\right)\right)\times\left(\dfrac{-\dfrac{13}{3}}{\dfrac{9}{8}}-\dfrac{-9}{\dfrac{125}{3}}\right)\\&=&\left(-9+\dfrac{3833}{24}\right)\times\dfrac{31}{8}\times\left(0+\dfrac{47}{3}\right)\times\left(\dfrac{-\dfrac{13}{3}}{\dfrac{9}{8}}-\dfrac{-9}{\dfrac{125}{3}}\right)\\&=&\left(-9+\dfrac{3833}{24}\right)\times\dfrac{31}{8}\times\left(0+\dfrac{47}{3}\right)\times\left(-\dfrac{104}{27}-\dfrac{-9}{\dfrac{125}{3}}\right)\\&=&\left(-9+\dfrac{3833}{24}\right)\times\dfrac{31}{8}\times\left(0+\dfrac{47}{3}\right)\times\left(-\dfrac{104}{27}+\dfrac{27}{125}\right)\\&=&\dfrac{3617}{24}\times\dfrac{31}{8}\times\left(0+\dfrac{47}{3}\right)\times\left(-\dfrac{104}{27}+\dfrac{27}{125}\right)\\&=&\dfrac{3617}{24}\times\dfrac{31}{8}\times\dfrac{47}{3}\times\left(-\dfrac{104}{27}+\dfrac{27}{125}\right)\\&=&\dfrac{3617}{24}\times\dfrac{31}{8}\times\dfrac{47}{3}\times-\dfrac{12271}{3375}\\&=&\dfrac{112127}{192}\times\dfrac{47}{3}\times-\dfrac{12271}{3375}\\&=&\dfrac{112127}{192}\times-\dfrac{576737}{10125}\\&=&-\dfrac{64667789599}{1944000}\\
\end{eqnarray*}