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 \[\left(7\times\left(-3\right)+\dfrac{7}{2}\times\left(-\dfrac{50}{9}\right)+\left(-\dfrac{50}{9}+\dfrac{93}{2}-7\right)-\left(\dfrac{13}{2}+\dfrac{\dfrac{-\dfrac{111}{8}}{4}}{\dfrac{93}{2}}-\dfrac{111}{8}-\dfrac{111}{8}\right)\right)\times\left(7-\dfrac{7}{2}-\dfrac{\dfrac{-\dfrac{50}{9}}{-\dfrac{50}{9}+\dfrac{13}{2}}}{-3+\dfrac{13}{2}}\right)\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(7\times\left(-3\right)+\dfrac{7}{2}\times\left(-\dfrac{50}{9}\right)+\left(-\dfrac{50}{9}+\dfrac{93}{2}-7\right)-\left(\dfrac{13}{2}+\dfrac{\dfrac{-\dfrac{111}{8}}{4}}{\dfrac{93}{2}}-\dfrac{111}{8}-\dfrac{111}{8}\right)\right)\times\left(7-\dfrac{7}{2}-\dfrac{\dfrac{-\dfrac{50}{9}}{-\dfrac{50}{9}+\dfrac{13}{2}}}{-3+\dfrac{13}{2}}\right)=\dfrac{9066249}{118048}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(7\times\left(-3\right)+\dfrac{7}{2}\times\left(-\dfrac{50}{9}\right)+\left(-\dfrac{50}{9}+\dfrac{93}{2}-7\right)-\left(\dfrac{13}{2}+\dfrac{-\dfrac{111}{32}}{\dfrac{93}{2}}-\dfrac{111}{8}-\dfrac{111}{8}\right)\right)\times\left(7-\dfrac{7}{2}-\dfrac{\dfrac{-\dfrac{50}{9}}{-\dfrac{50}{9}+\dfrac{13}{2}}}{-3+\dfrac{13}{2}}\right)\\&=&\left(7\times\left(-3\right)+\dfrac{7}{2}\times\left(-\dfrac{50}{9}\right)+\left(-\dfrac{50}{9}+\dfrac{93}{2}-7\right)-\left(\dfrac{13}{2}-\dfrac{37}{496}-\dfrac{111}{8}-\dfrac{111}{8}\right)\right)\times\left(7-\dfrac{7}{2}-\dfrac{\dfrac{-\dfrac{50}{9}}{-\dfrac{50}{9}+\dfrac{13}{2}}}{-3+\dfrac{13}{2}}\right)\\&=&\left(7\times\left(-3\right)+\dfrac{7}{2}\times\left(-\dfrac{50}{9}\right)+\left(-\dfrac{50}{9}+\dfrac{93}{2}-7\right)-\left(\dfrac{13}{2}-\dfrac{37}{496}-\dfrac{111}{4}\right)\right)\times\left(7-\dfrac{7}{2}-\dfrac{\dfrac{-\dfrac{50}{9}}{-\dfrac{50}{9}+\dfrac{13}{2}}}{-3+\dfrac{13}{2}}\right)\\&=&\left(7\times\left(-3\right)+\dfrac{7}{2}\times\left(-\dfrac{50}{9}\right)+\left(\dfrac{737}{18}-7\right)-\left(\dfrac{13}{2}-\dfrac{37}{496}-\dfrac{111}{4}\right)\right)\times\left(7-\dfrac{7}{2}-\dfrac{\dfrac{-\dfrac{50}{9}}{-\dfrac{50}{9}+\dfrac{13}{2}}}{-3+\dfrac{13}{2}}\right)\\&=&\left(7\times\left(-3\right)+\dfrac{7}{2}\times\left(-\dfrac{50}{9}\right)+\dfrac{611}{18}-\left(\dfrac{13}{2}-\dfrac{37}{496}-\dfrac{111}{4}\right)\right)\times\left(7-\dfrac{7}{2}-\dfrac{\dfrac{-\dfrac{50}{9}}{-\dfrac{50}{9}+\dfrac{13}{2}}}{-3+\dfrac{13}{2}}\right)\\&=&\left(7\times\left(-3\right)+\dfrac{7}{2}\times\left(-\dfrac{50}{9}\right)+\dfrac{611}{18}-\left(\dfrac{3187}{496}-\dfrac{111}{4}\right)\right)\times\left(7-\dfrac{7}{2}-\dfrac{\dfrac{-\dfrac{50}{9}}{-\dfrac{50}{9}+\dfrac{13}{2}}}{-3+\dfrac{13}{2}}\right)\\&=&\left(7\times\left(-3\right)+\dfrac{7}{2}\times\left(-\dfrac{50}{9}\right)+\dfrac{611}{18}+\dfrac{10577}{496}\right)\times\left(7-\dfrac{7}{2}-\dfrac{\dfrac{-\dfrac{50}{9}}{-\dfrac{50}{9}+\dfrac{13}{2}}}{-3+\dfrac{13}{2}}\right)\\&=&\left(7\times\left(-3\right)+\dfrac{7}{2}\times\left(-\dfrac{50}{9}\right)+\dfrac{611}{18}+\dfrac{10577}{496}\right)\times\left(7-\dfrac{7}{2}-\dfrac{\dfrac{-\dfrac{50}{9}}{\dfrac{17}{18}}}{-3+\dfrac{13}{2}}\right)\\&=&\left(7\times\left(-3\right)+\dfrac{7}{2}\times\left(-\dfrac{50}{9}\right)+\dfrac{611}{18}+\dfrac{10577}{496}\right)\times\left(7-\dfrac{7}{2}-\dfrac{\dfrac{-\dfrac{50}{9}}{\dfrac{17}{18}}}{\dfrac{7}{2}}\right)\\&=&\left(-21+\dfrac{7}{2}\times\left(-\dfrac{50}{9}\right)+\dfrac{611}{18}+\dfrac{10577}{496}\right)\times\left(7-\dfrac{7}{2}-\dfrac{\dfrac{-\dfrac{50}{9}}{\dfrac{17}{18}}}{\dfrac{7}{2}}\right)\\&=&\left(-21-\dfrac{175}{9}+\dfrac{611}{18}+\dfrac{10577}{496}\right)\times\left(7-\dfrac{7}{2}-\dfrac{\dfrac{-\dfrac{50}{9}}{\dfrac{17}{18}}}{\dfrac{7}{2}}\right)\\&=&\left(-21-\dfrac{175}{9}+\dfrac{246721}{4464}\right)\times\left(7-\dfrac{7}{2}-\dfrac{\dfrac{-\dfrac{50}{9}}{\dfrac{17}{18}}}{\dfrac{7}{2}}\right)\\&=&\left(-21-\dfrac{175}{9}+\dfrac{246721}{4464}\right)\times\left(7-\dfrac{7}{2}-\dfrac{-\dfrac{100}{17}}{\dfrac{7}{2}}\right)\\&=&\left(-21-\dfrac{175}{9}+\dfrac{246721}{4464}\right)\times\left(7-\dfrac{7}{2}+\dfrac{200}{119}\right)\\&=&\left(-\dfrac{364}{9}+\dfrac{246721}{4464}\right)\times\left(7-\dfrac{7}{2}+\dfrac{200}{119}\right)\\&=&\dfrac{7353}{496}\times\left(7-\dfrac{7}{2}+\dfrac{200}{119}\right)\\&=&\dfrac{7353}{496}\times\left(\dfrac{7}{2}+\dfrac{200}{119}\right)\\&=&\dfrac{7353}{496}\times\dfrac{1233}{238}\\&=&\dfrac{9066249}{118048}\\
\end{eqnarray*}