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 \[\left(-\dfrac{17}{5}\right)\times\left(-\dfrac{9}{2}+\dfrac{29}{6}-\dfrac{17}{3}-\dfrac{9}{2}\right)\times\left(-\dfrac{9}{2}\right)\times\left(\left(\dfrac{11}{2}-\dfrac{29}{6}+\dfrac{17}{3}\right)\times\left(-\dfrac{9}{2}\right)\times\dfrac{17}{4}\times\left(-\dfrac{17}{5}\right)-\dfrac{17}{4}\times\dfrac{29}{6}\times\dfrac{29}{6}-\dfrac{29}{6}\right)\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(-\dfrac{17}{5}\right)\times\left(-\dfrac{9}{2}+\dfrac{29}{6}-\dfrac{17}{3}-\dfrac{9}{2}\right)\times\left(-\dfrac{9}{2}\right)\times\left(\left(\dfrac{11}{2}-\dfrac{29}{6}+\dfrac{17}{3}\right)\times\left(-\dfrac{9}{2}\right)\times\dfrac{17}{4}\times\left(-\dfrac{17}{5}\right)-\dfrac{17}{4}\times\dfrac{29}{6}\times\dfrac{29}{6}-\dfrac{29}{6}\right)=-\dfrac{222213647}{4800}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-\dfrac{17}{5}\right)\times\left(\dfrac{1}{3}-\dfrac{17}{3}-\dfrac{9}{2}\right)\times\left(-\dfrac{9}{2}\right)\times\left(\left(\dfrac{11}{2}-\dfrac{29}{6}+\dfrac{17}{3}\right)\times\left(-\dfrac{9}{2}\right)\times\dfrac{17}{4}\times\left(-\dfrac{17}{5}\right)-\dfrac{17}{4}\times\dfrac{29}{6}\times\dfrac{29}{6}-\dfrac{29}{6}\right)\\&=&\left(-\dfrac{17}{5}\right)\times\left(-\dfrac{16}{3}-\dfrac{9}{2}\right)\times\left(-\dfrac{9}{2}\right)\times\left(\left(\dfrac{11}{2}-\dfrac{29}{6}+\dfrac{17}{3}\right)\times\left(-\dfrac{9}{2}\right)\times\dfrac{17}{4}\times\left(-\dfrac{17}{5}\right)-\dfrac{17}{4}\times\dfrac{29}{6}\times\dfrac{29}{6}-\dfrac{29}{6}\right)\\&=&\left(-\dfrac{17}{5}\right)\times\left(-\dfrac{16}{3}-\dfrac{9}{2}\right)\times\left(-\dfrac{9}{2}\right)\times\left(\left(\dfrac{2}{3}+\dfrac{17}{3}\right)\times\left(-\dfrac{9}{2}\right)\times\dfrac{17}{4}\times\left(-\dfrac{17}{5}\right)-\dfrac{17}{4}\times\dfrac{29}{6}\times\dfrac{29}{6}-\dfrac{29}{6}\right)\\&=&\left(-\dfrac{17}{5}\right)\times\left(-\dfrac{16}{3}-\dfrac{9}{2}\right)\times\left(-\dfrac{9}{2}\right)\times\left(\dfrac{19}{3}\times\left(-\dfrac{9}{2}\right)\times\dfrac{17}{4}\times\left(-\dfrac{17}{5}\right)-\dfrac{17}{4}\times\dfrac{29}{6}\times\dfrac{29}{6}-\dfrac{29}{6}\right)\\&=&\left(-\dfrac{17}{5}\right)\times\left(-\dfrac{16}{3}-\dfrac{9}{2}\right)\times\left(-\dfrac{9}{2}\right)\times\left(\dfrac{19}{3}\times\left(-\dfrac{9}{2}\right)\times\left(-\dfrac{289}{20}\right)-\dfrac{17}{4}\times\dfrac{29}{6}\times\dfrac{29}{6}-\dfrac{29}{6}\right)\\&=&\left(-\dfrac{17}{5}\right)\times-\dfrac{59}{6}\times\left(-\dfrac{9}{2}\right)\times\left(\dfrac{19}{3}\times\left(-\dfrac{9}{2}\right)\times\left(-\dfrac{289}{20}\right)-\dfrac{17}{4}\times\dfrac{29}{6}\times\dfrac{29}{6}-\dfrac{29}{6}\right)\\&=&\left(-\dfrac{17}{5}\right)\times-\dfrac{59}{6}\times\left(-\dfrac{9}{2}\right)\times\left(\left(-\dfrac{57}{2}\right)\times\left(-\dfrac{289}{20}\right)-\dfrac{17}{4}\times\dfrac{29}{6}\times\dfrac{29}{6}-\dfrac{29}{6}\right)\\&=&\left(-\dfrac{17}{5}\right)\times-\dfrac{59}{6}\times\left(-\dfrac{9}{2}\right)\times\left(\dfrac{16473}{40}-\dfrac{17}{4}\times\dfrac{29}{6}\times\dfrac{29}{6}-\dfrac{29}{6}\right)\\&=&\left(-\dfrac{17}{5}\right)\times-\dfrac{59}{6}\times\left(-\dfrac{9}{2}\right)\times\left(\dfrac{16473}{40}-\dfrac{493}{24}\times\dfrac{29}{6}-\dfrac{29}{6}\right)\\&=&\left(-\dfrac{17}{5}\right)\times-\dfrac{59}{6}\times\left(-\dfrac{9}{2}\right)\times\left(\dfrac{16473}{40}-\dfrac{14297}{144}-\dfrac{29}{6}\right)\\&=&\left(\dfrac{1003}{30}\right)\times\left(-\dfrac{9}{2}\right)\times\left(\dfrac{16473}{40}-\dfrac{14297}{144}-\dfrac{29}{6}\right)\\&=&\left(-\dfrac{3009}{20}\right)\times\left(\dfrac{16473}{40}-\dfrac{14297}{144}-\dfrac{29}{6}\right)\\&=&\left(-\dfrac{3009}{20}\right)\times\left(\dfrac{225029}{720}-\dfrac{29}{6}\right)\\&=&\left(-\dfrac{3009}{20}\right)\times\dfrac{221549}{720}\\&=&-\dfrac{222213647}{4800}\\
\end{eqnarray*}