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 \[\left(-\dfrac{33}{5}\right)\times\left(11+12-11+\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{130}{9}}{\dfrac{130}{9}}}{\dfrac{7}{4}}}{7}}{-\dfrac{69}{4}}\times11\right)\times\left(11-\left(5-11-11\right)-\dfrac{\dfrac{11\times\dfrac{-\dfrac{69}{4}}{11}\times\dfrac{130}{9}}{\left(5-\dfrac{130}{9}-11\right)-\left(-\dfrac{13}{10}-\dfrac{130}{9}\right)}}{\dfrac{90}{11}}\right)\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(-\dfrac{33}{5}\right)\times\left(11+12-11+\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{130}{9}}{\dfrac{130}{9}}}{\dfrac{7}{4}}}{7}}{-\dfrac{69}{4}}\times11\right)\times\left(11-\left(5-11-11\right)-\dfrac{\dfrac{11\times\dfrac{-\dfrac{69}{4}}{11}\times\dfrac{130}{9}}{\left(5-\dfrac{130}{9}-11\right)-\left(-\dfrac{13}{10}-\dfrac{130}{9}\right)}}{\dfrac{90}{11}}\right)=-\dfrac{24270280364}{14301630}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-\dfrac{33}{5}\right)\times\left(11+12-11+\dfrac{\dfrac{\dfrac{1}{\dfrac{7}{4}}}{7}}{-\dfrac{69}{4}}\times11\right)\times\left(11-\left(5-11-11\right)-\dfrac{\dfrac{11\times\dfrac{-\dfrac{69}{4}}{11}\times\dfrac{130}{9}}{\left(5-\dfrac{130}{9}-11\right)-\left(-\dfrac{13}{10}-\dfrac{130}{9}\right)}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+12-11+\dfrac{\dfrac{\dfrac{4}{7}}{7}}{-\dfrac{69}{4}}\times11\right)\times\left(11-\left(5-11-11\right)-\dfrac{\dfrac{11\times\dfrac{-\dfrac{69}{4}}{11}\times\dfrac{130}{9}}{\left(5-\dfrac{130}{9}-11\right)-\left(-\dfrac{13}{10}-\dfrac{130}{9}\right)}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+12-11+\dfrac{\dfrac{\dfrac{4}{7}}{7}}{-\dfrac{69}{4}}\times11\right)\times\left(11-\left(5-11-11\right)-\dfrac{\dfrac{11\times\left(-\dfrac{69}{44}\right)\times\dfrac{130}{9}}{\left(5-\dfrac{130}{9}-11\right)-\left(-\dfrac{13}{10}-\dfrac{130}{9}\right)}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+12-11+\dfrac{\dfrac{\dfrac{4}{7}}{7}}{-\dfrac{69}{4}}\times11\right)\times\left(11-\left(5-11-11\right)-\dfrac{\dfrac{11\times\left(-\dfrac{69}{44}\right)\times\dfrac{130}{9}}{\left(-\dfrac{85}{9}-11\right)-\left(-\dfrac{13}{10}-\dfrac{130}{9}\right)}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+12-11+\dfrac{\dfrac{\dfrac{4}{7}}{7}}{-\dfrac{69}{4}}\times11\right)\times\left(11-\left(5-11-11\right)-\dfrac{\dfrac{11\times\left(-\dfrac{69}{44}\right)\times\dfrac{130}{9}}{-\dfrac{184}{9}-\left(-\dfrac{13}{10}-\dfrac{130}{9}\right)}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+12-11+\dfrac{\dfrac{\dfrac{4}{7}}{7}}{-\dfrac{69}{4}}\times11\right)\times\left(11-\left(5-11-11\right)-\dfrac{\dfrac{11\times\left(-\dfrac{69}{44}\right)\times\dfrac{130}{9}}{-\dfrac{184}{9}+\dfrac{1417}{90}}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+12-11+\dfrac{\dfrac{4}{49}}{-\dfrac{69}{4}}\times11\right)\times\left(11-\left(5-11-11\right)-\dfrac{\dfrac{11\times\left(-\dfrac{69}{44}\right)\times\dfrac{130}{9}}{-\dfrac{184}{9}+\dfrac{1417}{90}}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+12-11+\left(-\dfrac{16}{3381}\right)\times11\right)\times\left(11-\left(5-11-11\right)-\dfrac{\dfrac{11\times\left(-\dfrac{69}{44}\right)\times\dfrac{130}{9}}{-\dfrac{184}{9}+\dfrac{1417}{90}}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+12-11+\left(-\dfrac{16}{3381}\right)\times11\right)\times\left(11-\left(5-11-11\right)-\dfrac{\dfrac{\left(-\dfrac{69}{4}\right)\times\dfrac{130}{9}}{-\dfrac{184}{9}+\dfrac{1417}{90}}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+12-11+\left(-\dfrac{16}{3381}\right)\times11\right)\times\left(11-\left(5-11-11\right)-\dfrac{\dfrac{-\dfrac{1495}{6}}{-\dfrac{184}{9}+\dfrac{1417}{90}}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+12-11+\left(-\dfrac{16}{3381}\right)\times11\right)\times\left(11-\left(5-11-11\right)-\dfrac{\dfrac{-\dfrac{1495}{6}}{-\dfrac{47}{10}}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+1+\left(-\dfrac{16}{3381}\right)\times11\right)\times\left(11-\left(5-11-11\right)-\dfrac{\dfrac{-\dfrac{1495}{6}}{-\dfrac{47}{10}}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+1-\dfrac{176}{3381}\right)\times\left(11-\left(5-11-11\right)-\dfrac{\dfrac{-\dfrac{1495}{6}}{-\dfrac{47}{10}}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+1-\dfrac{176}{3381}\right)\times\left(11-\left(-6-11\right)-\dfrac{\dfrac{-\dfrac{1495}{6}}{-\dfrac{47}{10}}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+1-\dfrac{176}{3381}\right)\times\left(11+17-\dfrac{\dfrac{-\dfrac{1495}{6}}{-\dfrac{47}{10}}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+1-\dfrac{176}{3381}\right)\times\left(11+17-\dfrac{\dfrac{7475}{141}}{\dfrac{90}{11}}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(11+1-\dfrac{176}{3381}\right)\times\left(11+17-\dfrac{16445}{2538}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\left(12-\dfrac{176}{3381}\right)\times\left(11+17-\dfrac{16445}{2538}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\dfrac{40396}{3381}\times\left(11+17-\dfrac{16445}{2538}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\dfrac{40396}{3381}\times\left(28-\dfrac{16445}{2538}\right)\\&=&\left(-\dfrac{33}{5}\right)\times\dfrac{40396}{3381}\times\dfrac{54619}{2538}\\&=&\left(-\dfrac{444356}{5635}\right)\times\dfrac{54619}{2538}\\&=&-\dfrac{24270280364}{14301630}\\
\end{eqnarray*}