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 \[12-11+\left(-\dfrac{118}{3}\right)\times\left(-\dfrac{118}{3}\right)\times\dfrac{6}{-11}\times\dfrac{33}{4}\times\left(-\dfrac{27}{11}\right)\times\left(-\dfrac{18}{5}\right)+\dfrac{75}{8}+\dfrac{-4+\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{75}{8}}{-\dfrac{118}{3}}}{-\dfrac{118}{3}}}{\dfrac{55}{4}}}{-11-6+\dfrac{27}{11}}+\dfrac{\dfrac{-\dfrac{27}{11}}{-\dfrac{132}{5}}}{-\dfrac{18}{5}}}{-4}-3\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=12-11+\left(-\dfrac{118}{3}\right)\times\left(-\dfrac{118}{3}\right)\times\dfrac{6}{-11}\times\dfrac{33}{4}\times\left(-\dfrac{27}{11}\right)\times\left(-\dfrac{18}{5}\right)+\dfrac{75}{8}+\dfrac{-4+\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{75}{8}}{-\dfrac{118}{3}}}{-\dfrac{118}{3}}}{\dfrac{55}{4}}}{-11-6+\dfrac{27}{11}}+\dfrac{\dfrac{-\dfrac{27}{11}}{-\dfrac{132}{5}}}{-\dfrac{18}{5}}}{-4}-3=-\dfrac{93385713023168192}{1518210580480}\) . Voici le détail :
\begin{eqnarray*}
X &=&12-11+\left(-\dfrac{118}{3}\right)\times\left(-\dfrac{118}{3}\right)\times\left(-\dfrac{6}{11}\right)\times\dfrac{33}{4}\times\left(-\dfrac{27}{11}\right)\times\left(-\dfrac{18}{5}\right)+\dfrac{75}{8}+\dfrac{-4+\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{75}{8}}{-\dfrac{118}{3}}}{-\dfrac{118}{3}}}{\dfrac{55}{4}}}{-11-6+\dfrac{27}{11}}+\dfrac{\dfrac{-\dfrac{27}{11}}{-\dfrac{132}{5}}}{-\dfrac{18}{5}}}{-4}-3\\&=&12-11+\left(-\dfrac{118}{3}\right)\times\left(-\dfrac{118}{3}\right)\times\left(-\dfrac{6}{11}\right)\times\dfrac{33}{4}\times\left(-\dfrac{27}{11}\right)\times\left(-\dfrac{18}{5}\right)+\dfrac{75}{8}+\dfrac{-4+\dfrac{\dfrac{\dfrac{-\dfrac{225}{944}}{-\dfrac{118}{3}}}{\dfrac{55}{4}}}{-11-6+\dfrac{27}{11}}+\dfrac{\dfrac{-\dfrac{27}{11}}{-\dfrac{132}{5}}}{-\dfrac{18}{5}}}{-4}-3\\&=&12-11+\left(-\dfrac{118}{3}\right)\times\left(-\dfrac{118}{3}\right)\times\left(-\dfrac{6}{11}\right)\times\dfrac{33}{4}\times\left(-\dfrac{27}{11}\right)\times\left(-\dfrac{18}{5}\right)+\dfrac{75}{8}+\dfrac{-4+\dfrac{\dfrac{\dfrac{-\dfrac{225}{944}}{-\dfrac{118}{3}}}{\dfrac{55}{4}}}{-17+\dfrac{27}{11}}+\dfrac{\dfrac{-\dfrac{27}{11}}{-\dfrac{132}{5}}}{-\dfrac{18}{5}}}{-4}-3\\&=&12-11+\left(-\dfrac{118}{3}\right)\times\left(-\dfrac{118}{3}\right)\times\left(-\dfrac{6}{11}\right)\times\dfrac{33}{4}\times\left(-\dfrac{27}{11}\right)\times\left(-\dfrac{18}{5}\right)+\dfrac{75}{8}+\dfrac{-4+\dfrac{\dfrac{\dfrac{-\dfrac{225}{944}}{-\dfrac{118}{3}}}{\dfrac{55}{4}}}{-\dfrac{160}{11}}+\dfrac{\dfrac{-\dfrac{27}{11}}{-\dfrac{132}{5}}}{-\dfrac{18}{5}}}{-4}-3\\&=&12-11+\dfrac{13924}{9}\times\left(-\dfrac{6}{11}\right)\times\dfrac{33}{4}\times\left(-\dfrac{27}{11}\right)\times\left(-\dfrac{18}{5}\right)+\dfrac{75}{8}+\dfrac{-4+\dfrac{\dfrac{\dfrac{-\dfrac{225}{944}}{-\dfrac{118}{3}}}{\dfrac{55}{4}}}{-\dfrac{160}{11}}+\dfrac{\dfrac{-\dfrac{27}{11}}{-\dfrac{132}{5}}}{-\dfrac{18}{5}}}{-4}-3\\&=&12-11+\left(-\dfrac{27848}{33}\right)\times\dfrac{33}{4}\times\left(-\dfrac{27}{11}\right)\times\left(-\dfrac{18}{5}\right)+\dfrac{75}{8}+\dfrac{-4+\dfrac{\dfrac{\dfrac{-\dfrac{225}{944}}{-\dfrac{118}{3}}}{\dfrac{55}{4}}}{-\dfrac{160}{11}}+\dfrac{\dfrac{-\dfrac{27}{11}}{-\dfrac{132}{5}}}{-\dfrac{18}{5}}}{-4}-3\\&=&12-11+\left(-\dfrac{27848}{33}\right)\times\dfrac{33}{4}\times\left(-\dfrac{27}{11}\right)\times\left(-\dfrac{18}{5}\right)+\dfrac{75}{8}+\dfrac{-4+\dfrac{\dfrac{\dfrac{675}{111392}}{\dfrac{55}{4}}}{-\dfrac{160}{11}}+\dfrac{\dfrac{-\dfrac{27}{11}}{-\dfrac{132}{5}}}{-\dfrac{18}{5}}}{-4}-3\\&=&12-11+\left(-\dfrac{27848}{33}\right)\times\dfrac{33}{4}\times\left(-\dfrac{27}{11}\right)\times\left(-\dfrac{18}{5}\right)+\dfrac{75}{8}+\dfrac{-4+\dfrac{\dfrac{135}{306328}}{-\dfrac{160}{11}}+\dfrac{\dfrac{-\dfrac{27}{11}}{-\dfrac{132}{5}}}{-\dfrac{18}{5}}}{-4}-3\\&=&12-11+\left(-\dfrac{27848}{33}\right)\times\dfrac{33}{4}\times\left(-\dfrac{27}{11}\right)\times\left(-\dfrac{18}{5}\right)+\dfrac{75}{8}+\dfrac{-4-\dfrac{27}{891136}+\dfrac{\dfrac{-\dfrac{27}{11}}{-\dfrac{132}{5}}}{-\dfrac{18}{5}}}{-4}-3\\&=&12-11+\left(-\dfrac{27848}{33}\right)\times\dfrac{33}{4}\times\left(-\dfrac{27}{11}\right)\times\left(-\dfrac{18}{5}\right)+\dfrac{75}{8}+\dfrac{-4-\dfrac{27}{891136}+\dfrac{\dfrac{45}{484}}{-\dfrac{18}{5}}}{-4}-3\\&=&12-11+\left(-\dfrac{27848}{33}\right)\times\dfrac{33}{4}\times\left(-\dfrac{27}{11}\right)\times\left(-\dfrac{18}{5}\right)+\dfrac{75}{8}+\dfrac{-4-\dfrac{27}{891136}-\dfrac{25}{968}}{-4}-3\\&=&12-11+\left(-6962\right)\times\left(-\dfrac{27}{11}\right)\times\left(-\dfrac{18}{5}\right)+\dfrac{75}{8}+\dfrac{-4-\dfrac{27}{891136}-\dfrac{25}{968}}{-4}-3\\&=&12-11+\dfrac{187974}{11}\times\left(-\dfrac{18}{5}\right)+\dfrac{75}{8}+\dfrac{-4-\dfrac{27}{891136}-\dfrac{25}{968}}{-4}-3\\&=&12-11-\dfrac{3383532}{55}+\dfrac{75}{8}+\dfrac{-4-\dfrac{27}{891136}-\dfrac{25}{968}}{-4}-3\\&=&12-11-\dfrac{3383532}{55}+\dfrac{75}{8}+\dfrac{-\dfrac{3564571}{891136}-\dfrac{25}{968}}{-4}-3\\&=&12-11-\dfrac{3383532}{55}+\dfrac{75}{8}+\dfrac{-\dfrac{3472783128}{862619648}}{-4}-3\\&=&1-\dfrac{3383532}{55}+\dfrac{75}{8}+\dfrac{-\dfrac{3472783128}{862619648}}{-4}-3\\&=&-\dfrac{3383477}{55}+\dfrac{75}{8}+\dfrac{-\dfrac{3472783128}{862619648}}{-4}-3\\&=&-\dfrac{3383477}{55}+\dfrac{75}{8}+\dfrac{3472783128}{3450478592}-3\\&=&-\dfrac{27063691}{440}+\dfrac{3472783128}{3450478592}-3\\&=&-\dfrac{93381158391426752}{1518210580480}-3\\&=&-\dfrac{93385713023168192}{1518210580480}\\
\end{eqnarray*}