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 \[\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\dfrac{93}{10}\times\dfrac{\dfrac{\dfrac{-\dfrac{7}{4}}{-\dfrac{8}{5}}}{12}}{5}\times\left(-\dfrac{133}{5}\right)\times\left(-\dfrac{113}{2}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{133}{5}}{-\dfrac{113}{2}}}{-\dfrac{8}{5}-7+\dfrac{59}{6}}}{-\dfrac{40}{7}}\times12\times\left(-12\right)}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\dfrac{93}{10}\times\dfrac{\dfrac{\dfrac{-\dfrac{7}{4}}{-\dfrac{8}{5}}}{12}}{5}\times\left(-\dfrac{133}{5}\right)\times\left(-\dfrac{113}{2}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{133}{5}}{-\dfrac{113}{2}}}{-\dfrac{8}{5}-7+\dfrac{59}{6}}}{-\dfrac{40}{7}}\times12\times\left(-12\right)}=-\dfrac{110112000}{46430653248}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\dfrac{93}{10}\times\dfrac{\dfrac{\dfrac{-\dfrac{7}{4}}{-\dfrac{8}{5}}}{12}}{5}\times\left(-\dfrac{133}{5}\right)\times\left(-\dfrac{113}{2}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{133}{5}}{-\dfrac{113}{2}}}{-\dfrac{43}{5}+\dfrac{59}{6}}}{-\dfrac{40}{7}}\times12\times\left(-12\right)}\\&=&\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\dfrac{93}{10}\times\dfrac{\dfrac{\dfrac{-\dfrac{7}{4}}{-\dfrac{8}{5}}}{12}}{5}\times\left(-\dfrac{133}{5}\right)\times\left(-\dfrac{113}{2}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{133}{5}}{-\dfrac{113}{2}}}{\dfrac{37}{30}}}{-\dfrac{40}{7}}\times12\times\left(-12\right)}\\&=&\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\dfrac{93}{10}\times\dfrac{\dfrac{\dfrac{-\dfrac{7}{4}}{-\dfrac{8}{5}}}{12}}{5}\times\left(-\dfrac{133}{5}\right)\times\left(-\dfrac{113}{2}\right)\times\dfrac{\dfrac{\dfrac{266}{565}}{\dfrac{37}{30}}}{-\dfrac{40}{7}}\times12\times\left(-12\right)}\\&=&\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\dfrac{93}{10}\times\dfrac{\dfrac{\dfrac{-\dfrac{7}{4}}{-\dfrac{8}{5}}}{12}}{5}\times\left(-\dfrac{133}{5}\right)\times\left(-\dfrac{113}{2}\right)\times\dfrac{\dfrac{1596}{4181}}{-\dfrac{40}{7}}\times12\times\left(-12\right)}\\&=&\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\dfrac{93}{10}\times\dfrac{\dfrac{\dfrac{-\dfrac{7}{4}}{-\dfrac{8}{5}}}{12}}{5}\times\left(-\dfrac{133}{5}\right)\times\left(-\dfrac{113}{2}\right)\times\left(-\dfrac{2793}{41810}\right)\times12\times\left(-12\right)}\\&=&\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\dfrac{93}{10}\times\dfrac{\dfrac{\dfrac{35}{32}}{12}}{5}\times\left(-\dfrac{133}{5}\right)\times\left(-\dfrac{113}{2}\right)\times\left(-\dfrac{2793}{41810}\right)\times12\times\left(-12\right)}\\&=&\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\dfrac{93}{10}\times\dfrac{\dfrac{35}{384}}{5}\times\left(-\dfrac{133}{5}\right)\times\left(-\dfrac{113}{2}\right)\times\left(-\dfrac{2793}{41810}\right)\times12\times\left(-12\right)}\\&=&\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\dfrac{93}{10}\times\dfrac{7}{384}\times\left(-\dfrac{133}{5}\right)\times\left(-\dfrac{113}{2}\right)\times\left(-\dfrac{2793}{41810}\right)\times12\times\left(-12\right)}\\&=&\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\dfrac{93}{10}\times\dfrac{7}{384}\times\dfrac{15029}{10}\times\left(-\dfrac{2793}{41810}\right)\times12\times\left(-12\right)}\\&=&\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\dfrac{93}{10}\times\dfrac{7}{384}\times\left(-\dfrac{371469}{3700}\right)\times12\times\left(-12\right)}\\&=&\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\dfrac{93}{10}\times\dfrac{7}{384}\times\left(-\dfrac{1114407}{925}\right)\times\left(-12\right)}\\&=&\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\dfrac{217}{1280}\times\left(-\dfrac{1114407}{925}\right)\times\left(-12\right)}\\&=&\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\left(-\dfrac{241826319}{1184000}\right)\times\left(-12\right)}\\&=&\dfrac{\dfrac{\dfrac{93}{10}}{-\dfrac{8}{5}}}{\dfrac{2901915828}{1184000}}\\&=&\dfrac{-\dfrac{93}{16}}{\dfrac{2901915828}{1184000}}\\&=&-\dfrac{110112000}{46430653248}\\
\end{eqnarray*}