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 \[\left(\dfrac{-\dfrac{70}{3}}{\dfrac{141}{11}}+\dfrac{\dfrac{\dfrac{-\dfrac{70}{3}}{-1}}{-\dfrac{35}{6}}}{\dfrac{141}{11}}-\dfrac{89}{10}-\dfrac{74}{3}-\dfrac{109}{3}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\left(-1\right)\times\left(-\dfrac{45}{4}-\dfrac{89}{10}\right)\times\left(\dfrac{141}{11}+\dfrac{74}{3}\right)\times\dfrac{55}{4}\times\left(-\dfrac{109}{3}\right)\times\left(-1\right)}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(\dfrac{-\dfrac{70}{3}}{\dfrac{141}{11}}+\dfrac{\dfrac{\dfrac{-\dfrac{70}{3}}{-1}}{-\dfrac{35}{6}}}{\dfrac{141}{11}}-\dfrac{89}{10}-\dfrac{74}{3}-\dfrac{109}{3}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\left(-1\right)\times\left(-\dfrac{45}{4}-\dfrac{89}{10}\right)\times\left(\dfrac{141}{11}+\dfrac{74}{3}\right)\times\dfrac{55}{4}\times\left(-\dfrac{109}{3}\right)\times\left(-1\right)}=-\dfrac{74562523200}{25283331344700}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(\dfrac{-\dfrac{70}{3}}{\dfrac{141}{11}}+\dfrac{\dfrac{\dfrac{70}{3}}{-\dfrac{35}{6}}}{\dfrac{141}{11}}-\dfrac{89}{10}-\dfrac{74}{3}-\dfrac{109}{3}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\left(-1\right)\times\left(-\dfrac{45}{4}-\dfrac{89}{10}\right)\times\left(\dfrac{141}{11}+\dfrac{74}{3}\right)\times\dfrac{55}{4}\times\left(-\dfrac{109}{3}\right)\times\left(-1\right)}\\&=&\left(\dfrac{-\dfrac{70}{3}}{\dfrac{141}{11}}+\dfrac{-4}{\dfrac{141}{11}}-\dfrac{89}{10}-\dfrac{74}{3}-\dfrac{109}{3}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\left(-1\right)\times\left(-\dfrac{45}{4}-\dfrac{89}{10}\right)\times\left(\dfrac{141}{11}+\dfrac{74}{3}\right)\times\dfrac{55}{4}\times\left(-\dfrac{109}{3}\right)\times\left(-1\right)}\\&=&\left(\dfrac{-\dfrac{70}{3}}{\dfrac{141}{11}}+\dfrac{-4}{\dfrac{141}{11}}-\dfrac{89}{10}-\dfrac{74}{3}-\dfrac{109}{3}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\left(-1\right)\times\left(-\dfrac{403}{20}\right)\times\left(\dfrac{141}{11}+\dfrac{74}{3}\right)\times\dfrac{55}{4}\times\left(-\dfrac{109}{3}\right)\times\left(-1\right)}\\&=&\left(\dfrac{-\dfrac{70}{3}}{\dfrac{141}{11}}+\dfrac{-4}{\dfrac{141}{11}}-\dfrac{89}{10}-\dfrac{74}{3}-\dfrac{109}{3}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\left(-1\right)\times\left(-\dfrac{403}{20}\right)\times\dfrac{1237}{33}\times\dfrac{55}{4}\times\left(-\dfrac{109}{3}\right)\times\left(-1\right)}\\&=&\left(-\dfrac{770}{423}+\dfrac{-4}{\dfrac{141}{11}}-\dfrac{89}{10}-\dfrac{74}{3}-\dfrac{109}{3}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\left(-1\right)\times\left(-\dfrac{403}{20}\right)\times\dfrac{1237}{33}\times\dfrac{55}{4}\times\left(-\dfrac{109}{3}\right)\times\left(-1\right)}\\&=&\left(-\dfrac{770}{423}-\dfrac{44}{141}-\dfrac{89}{10}-\dfrac{74}{3}-\dfrac{109}{3}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\left(-1\right)\times\left(-\dfrac{403}{20}\right)\times\dfrac{1237}{33}\times\dfrac{55}{4}\times\left(-\dfrac{109}{3}\right)\times\left(-1\right)}\\&=&\left(-\dfrac{770}{423}-\dfrac{44}{141}-\dfrac{1007}{30}-\dfrac{109}{3}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\left(-1\right)\times\left(-\dfrac{403}{20}\right)\times\dfrac{1237}{33}\times\dfrac{55}{4}\times\left(-\dfrac{109}{3}\right)\times\left(-1\right)}\\&=&\left(-\dfrac{770}{423}-\dfrac{44}{141}-\dfrac{699}{10}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\left(-1\right)\times\left(-\dfrac{403}{20}\right)\times\dfrac{1237}{33}\times\dfrac{55}{4}\times\left(-\dfrac{109}{3}\right)\times\left(-1\right)}\\&=&\left(-\dfrac{770}{423}-\dfrac{44}{141}-\dfrac{699}{10}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\dfrac{403}{20}\times\dfrac{1237}{33}\times\dfrac{55}{4}\times\left(-\dfrac{109}{3}\right)\times\left(-1\right)}\\&=&\left(-\dfrac{770}{423}-\dfrac{44}{141}-\dfrac{699}{10}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\dfrac{498511}{660}\times\dfrac{55}{4}\times\left(-\dfrac{109}{3}\right)\times\left(-1\right)}\\&=&\left(-\dfrac{770}{423}-\dfrac{44}{141}-\dfrac{699}{10}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\dfrac{498511}{660}\times\left(-\dfrac{5995}{12}\right)\times\left(-1\right)}\\&=&\left(-\dfrac{902}{423}-\dfrac{699}{10}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\dfrac{498511}{660}\times\left(-\dfrac{5995}{12}\right)\times\left(-1\right)}\\&=&\left(-\dfrac{304697}{4230}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\dfrac{498511}{660}\times\left(-\dfrac{5995}{12}\right)\times\left(-1\right)}\\&=&\left(-\dfrac{304697}{4230}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\left(-\dfrac{2988573445}{7920}\right)\times\left(-1\right)}\\&=&\left(-\dfrac{304697}{4230}-\dfrac{89}{10}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\dfrac{2988573445}{7920}}\\&=&\left(-\dfrac{171172}{2115}\right)\times\left(-1\right)\times\dfrac{\dfrac{\dfrac{55}{4}}{-1}}{\dfrac{2988573445}{7920}}\\&=&\left(-\dfrac{171172}{2115}\right)\times\left(-1\right)\times\dfrac{-\dfrac{55}{4}}{\dfrac{2988573445}{7920}}\\&=&\left(-\dfrac{171172}{2115}\right)\times\left(-1\right)\times\left(-\dfrac{435600}{11954293780}\right)\\&=&\dfrac{171172}{2115}\times\left(-\dfrac{435600}{11954293780}\right)\\&=&-\dfrac{74562523200}{25283331344700}\\
\end{eqnarray*}