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 \[\left(-\dfrac{24}{7}\right)\times\dfrac{14}{3}\times\left(-\dfrac{79}{5}\right)\times\left(\left(\dfrac{41}{5}-\left(-\dfrac{24}{7}\right)\times\left(-7\right)\times\left(-7\right)-\dfrac{14}{3}\right)-\dfrac{140}{3}-\dfrac{\dfrac{-\dfrac{24}{7}}{4}}{\dfrac{\dfrac{\dfrac{3}{-12}}{3}}{3+\dfrac{37}{6}-\dfrac{126}{5}}}\right)\times\dfrac{140}{3}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(-\dfrac{24}{7}\right)\times\dfrac{14}{3}\times\left(-\dfrac{79}{5}\right)\times\left(\left(\dfrac{41}{5}-\left(-\dfrac{24}{7}\right)\times\left(-7\right)\times\left(-7\right)-\dfrac{14}{3}\right)-\dfrac{140}{3}-\dfrac{\dfrac{-\dfrac{24}{7}}{4}}{\dfrac{\dfrac{\dfrac{3}{-12}}{3}}{3+\dfrac{37}{6}-\dfrac{126}{5}}}\right)\times\dfrac{140}{3}=\dfrac{5384361920}{1575}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-\dfrac{24}{7}\right)\times\dfrac{14}{3}\times\left(-\dfrac{79}{5}\right)\times\left(\left(\dfrac{41}{5}-24\times\left(-7\right)-\dfrac{14}{3}\right)-\dfrac{140}{3}-\dfrac{\dfrac{-\dfrac{24}{7}}{4}}{\dfrac{\dfrac{\dfrac{3}{-12}}{3}}{3+\dfrac{37}{6}-\dfrac{126}{5}}}\right)\times\dfrac{140}{3}\\&=&\left(-\dfrac{24}{7}\right)\times\dfrac{14}{3}\times\left(-\dfrac{79}{5}\right)\times\left(\left(\dfrac{41}{5}-24\times\left(-7\right)-\dfrac{14}{3}\right)-\dfrac{140}{3}-\dfrac{\dfrac{-\dfrac{24}{7}}{4}}{\dfrac{\dfrac{-\dfrac{1}{4}}{3}}{3+\dfrac{37}{6}-\dfrac{126}{5}}}\right)\times\dfrac{140}{3}\\&=&\left(-\dfrac{24}{7}\right)\times\dfrac{14}{3}\times\left(-\dfrac{79}{5}\right)\times\left(\left(\dfrac{41}{5}-24\times\left(-7\right)-\dfrac{14}{3}\right)-\dfrac{140}{3}-\dfrac{\dfrac{-\dfrac{24}{7}}{4}}{\dfrac{-\dfrac{1}{12}}{3+\dfrac{37}{6}-\dfrac{126}{5}}}\right)\times\dfrac{140}{3}\\&=&\left(-\dfrac{24}{7}\right)\times\dfrac{14}{3}\times\left(-\dfrac{79}{5}\right)\times\left(\left(\dfrac{41}{5}-24\times\left(-7\right)-\dfrac{14}{3}\right)-\dfrac{140}{3}-\dfrac{\dfrac{-\dfrac{24}{7}}{4}}{\dfrac{-\dfrac{1}{12}}{\dfrac{55}{6}-\dfrac{126}{5}}}\right)\times\dfrac{140}{3}\\&=&\left(-\dfrac{24}{7}\right)\times\dfrac{14}{3}\times\left(-\dfrac{79}{5}\right)\times\left(\left(\dfrac{41}{5}-24\times\left(-7\right)-\dfrac{14}{3}\right)-\dfrac{140}{3}-\dfrac{\dfrac{-\dfrac{24}{7}}{4}}{\dfrac{-\dfrac{1}{12}}{-\dfrac{481}{30}}}\right)\times\dfrac{140}{3}\\&=&\left(-\dfrac{24}{7}\right)\times\dfrac{14}{3}\times\left(-\dfrac{79}{5}\right)\times\left(\left(\dfrac{41}{5}+168-\dfrac{14}{3}\right)-\dfrac{140}{3}-\dfrac{\dfrac{-\dfrac{24}{7}}{4}}{\dfrac{-\dfrac{1}{12}}{-\dfrac{481}{30}}}\right)\times\dfrac{140}{3}\\&=&\left(-\dfrac{24}{7}\right)\times\dfrac{14}{3}\times\left(-\dfrac{79}{5}\right)\times\left(\left(\dfrac{41}{5}+168-\dfrac{14}{3}\right)-\dfrac{140}{3}-\dfrac{\dfrac{-\dfrac{24}{7}}{4}}{\dfrac{5}{962}}\right)\times\dfrac{140}{3}\\&=&\left(-\dfrac{24}{7}\right)\times\dfrac{14}{3}\times\left(-\dfrac{79}{5}\right)\times\left(\left(\dfrac{881}{5}-\dfrac{14}{3}\right)-\dfrac{140}{3}-\dfrac{\dfrac{-\dfrac{24}{7}}{4}}{\dfrac{5}{962}}\right)\times\dfrac{140}{3}\\&=&\left(-\dfrac{24}{7}\right)\times\dfrac{14}{3}\times\left(-\dfrac{79}{5}\right)\times\left(\dfrac{2573}{15}-\dfrac{140}{3}-\dfrac{\dfrac{-\dfrac{24}{7}}{4}}{\dfrac{5}{962}}\right)\times\dfrac{140}{3}\\&=&\left(-\dfrac{24}{7}\right)\times\dfrac{14}{3}\times\left(-\dfrac{79}{5}\right)\times\left(\dfrac{2573}{15}-\dfrac{140}{3}-\dfrac{-\dfrac{6}{7}}{\dfrac{5}{962}}\right)\times\dfrac{140}{3}\\&=&\left(-\dfrac{24}{7}\right)\times\dfrac{14}{3}\times\left(-\dfrac{79}{5}\right)\times\left(\dfrac{2573}{15}-\dfrac{140}{3}+\dfrac{5772}{35}\right)\times\dfrac{140}{3}\\&=&\left(-16\right)\times\left(-\dfrac{79}{5}\right)\times\left(\dfrac{2573}{15}-\dfrac{140}{3}+\dfrac{5772}{35}\right)\times\dfrac{140}{3}\\&=&\dfrac{1264}{5}\times\left(\dfrac{2573}{15}-\dfrac{140}{3}+\dfrac{5772}{35}\right)\times\dfrac{140}{3}\\&=&\dfrac{1264}{5}\times\left(\dfrac{1873}{15}+\dfrac{5772}{35}\right)\times\dfrac{140}{3}\\&=&\dfrac{1264}{5}\times\dfrac{30427}{105}\times\dfrac{140}{3}\\&=&\dfrac{38459728}{525}\times\dfrac{140}{3}\\&=&\dfrac{5384361920}{1575}\\
\end{eqnarray*}