L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[-8-\left(-5\right)\times\left(-\dfrac{113}{5}-\dfrac{113}{5}-\dfrac{101}{7}+\dfrac{101}{7}-\dfrac{93}{8}\right)\times\dfrac{-\dfrac{113}{5}}{\dfrac{\dfrac{\dfrac{4}{-\dfrac{93}{8}}}{-\dfrac{101}{7}}}{-\dfrac{113}{5}}}\times4\times\left(-3\right)\times\left(-5-\left(-5-\dfrac{93}{8}\right)+\dfrac{113}{5}-\dfrac{\dfrac{\dfrac{55}{12}}{-5}}{-\dfrac{18}{5}-3}\right)-\left(\dfrac{55}{12}-5\right)+3\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=-8-\left(-5\right)\times\left(-\dfrac{113}{5}-\dfrac{113}{5}-\dfrac{101}{7}+\dfrac{101}{7}-\dfrac{93}{8}\right)\times\dfrac{-\dfrac{113}{5}}{\dfrac{\dfrac{\dfrac{4}{-\dfrac{93}{8}}}{-\dfrac{101}{7}}}{-\dfrac{113}{5}}}\times4\times\left(-3\right)\times\left(-5-\left(-5-\dfrac{93}{8}\right)+\dfrac{113}{5}-\dfrac{\dfrac{\dfrac{55}{12}}{-5}}{-\dfrac{18}{5}-3}\right)-\left(\dfrac{55}{12}-5\right)+3=\dfrac{481729333742972784}{193536000}\) . Voici le détail :
\begin{eqnarray*}
X &=&-8-\left(-5\right)\times\left(-\dfrac{113}{5}-\dfrac{113}{5}+0-\dfrac{93}{8}\right)\times\dfrac{-\dfrac{113}{5}}{\dfrac{\dfrac{\dfrac{4}{-\dfrac{93}{8}}}{-\dfrac{101}{7}}}{-\dfrac{113}{5}}}\times4\times\left(-3\right)\times\left(-5-\left(-5-\dfrac{93}{8}\right)+\dfrac{113}{5}-\dfrac{\dfrac{\dfrac{55}{12}}{-5}}{-\dfrac{18}{5}-3}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\left(-5\right)\times\left(-\dfrac{113}{5}-\dfrac{113}{5}+0-\dfrac{93}{8}\right)\times\dfrac{-\dfrac{113}{5}}{\dfrac{\dfrac{-\dfrac{32}{93}}{-\dfrac{101}{7}}}{-\dfrac{113}{5}}}\times4\times\left(-3\right)\times\left(-5-\left(-5-\dfrac{93}{8}\right)+\dfrac{113}{5}-\dfrac{\dfrac{\dfrac{55}{12}}{-5}}{-\dfrac{18}{5}-3}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\left(-5\right)\times\left(-\dfrac{113}{5}-\dfrac{113}{5}+0-\dfrac{93}{8}\right)\times\dfrac{-\dfrac{113}{5}}{\dfrac{\dfrac{224}{9393}}{-\dfrac{113}{5}}}\times4\times\left(-3\right)\times\left(-5-\left(-5-\dfrac{93}{8}\right)+\dfrac{113}{5}-\dfrac{\dfrac{\dfrac{55}{12}}{-5}}{-\dfrac{18}{5}-3}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\left(-5\right)\times\left(-\dfrac{113}{5}-\dfrac{113}{5}+0-\dfrac{93}{8}\right)\times\dfrac{-\dfrac{113}{5}}{-\dfrac{1120}{1061409}}\times4\times\left(-3\right)\times\left(-5-\left(-5-\dfrac{93}{8}\right)+\dfrac{113}{5}-\dfrac{\dfrac{\dfrac{55}{12}}{-5}}{-\dfrac{18}{5}-3}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\left(-5\right)\times\left(-\dfrac{113}{5}-\dfrac{113}{5}+0-\dfrac{93}{8}\right)\times\dfrac{-\dfrac{113}{5}}{-\dfrac{1120}{1061409}}\times4\times\left(-3\right)\times\left(-5-\left(-5-\dfrac{93}{8}\right)+\dfrac{113}{5}-\dfrac{\dfrac{\dfrac{55}{12}}{-5}}{-\dfrac{33}{5}}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\left(-5\right)\times\left(-\dfrac{226}{5}+0-\dfrac{93}{8}\right)\times\dfrac{-\dfrac{113}{5}}{-\dfrac{1120}{1061409}}\times4\times\left(-3\right)\times\left(-5-\left(-5-\dfrac{93}{8}\right)+\dfrac{113}{5}-\dfrac{\dfrac{\dfrac{55}{12}}{-5}}{-\dfrac{33}{5}}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\left(-5\right)\times\left(-\dfrac{226}{5}-\dfrac{93}{8}\right)\times\dfrac{-\dfrac{113}{5}}{-\dfrac{1120}{1061409}}\times4\times\left(-3\right)\times\left(-5-\left(-5-\dfrac{93}{8}\right)+\dfrac{113}{5}-\dfrac{\dfrac{\dfrac{55}{12}}{-5}}{-\dfrac{33}{5}}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\left(-5\right)\times-\dfrac{2273}{40}\times\dfrac{-\dfrac{113}{5}}{-\dfrac{1120}{1061409}}\times4\times\left(-3\right)\times\left(-5-\left(-5-\dfrac{93}{8}\right)+\dfrac{113}{5}-\dfrac{\dfrac{\dfrac{55}{12}}{-5}}{-\dfrac{33}{5}}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\left(-5\right)\times-\dfrac{2273}{40}\times\dfrac{119939217}{5600}\times4\times\left(-3\right)\times\left(-5-\left(-5-\dfrac{93}{8}\right)+\dfrac{113}{5}-\dfrac{\dfrac{\dfrac{55}{12}}{-5}}{-\dfrac{33}{5}}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\left(-5\right)\times-\dfrac{2273}{40}\times\dfrac{119939217}{5600}\times4\times\left(-3\right)\times\left(-5+\dfrac{133}{8}+\dfrac{113}{5}-\dfrac{\dfrac{\dfrac{55}{12}}{-5}}{-\dfrac{33}{5}}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\left(-5\right)\times-\dfrac{2273}{40}\times\dfrac{119939217}{5600}\times4\times\left(-3\right)\times\left(-5+\dfrac{133}{8}+\dfrac{113}{5}-\dfrac{-\dfrac{11}{12}}{-\dfrac{33}{5}}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\left(-5\right)\times-\dfrac{2273}{40}\times\dfrac{119939217}{5600}\times4\times\left(-3\right)\times\left(-5+\dfrac{133}{8}+\dfrac{113}{5}-\dfrac{5}{36}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\dfrac{2273}{8}\times\dfrac{119939217}{5600}\times4\times\left(-3\right)\times\left(-5+\dfrac{133}{8}+\dfrac{113}{5}-\dfrac{5}{36}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\dfrac{272621840241}{44800}\times4\times\left(-3\right)\times\left(-5+\dfrac{133}{8}+\dfrac{113}{5}-\dfrac{5}{36}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\dfrac{1090487360964}{44800}\times\left(-3\right)\times\left(-5+\dfrac{133}{8}+\dfrac{113}{5}-\dfrac{5}{36}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\dfrac{1090487360964}{44800}\times\left(-3\right)\times\left(\dfrac{93}{8}+\dfrac{113}{5}-\dfrac{5}{36}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\dfrac{1090487360964}{44800}\times\left(-3\right)\times\left(\dfrac{1369}{40}-\dfrac{5}{36}\right)-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\dfrac{1090487360964}{44800}\times\left(-3\right)\times\dfrac{12271}{360}-\left(\dfrac{55}{12}-5\right)+3\\&=&-8-\left(-\dfrac{3271462082892}{44800}\right)\times\dfrac{12271}{360}-\left(\dfrac{55}{12}-5\right)+3\\&=&-8+\dfrac{40144111219167732}{16128000}-\left(\dfrac{55}{12}-5\right)+3\\&=&-8+\dfrac{40144111219167732}{16128000}+\dfrac{5}{12}+3\\&=&\dfrac{40144111090143732}{16128000}+\dfrac{5}{12}+3\\&=&\dfrac{481729333162364784}{193536000}+3\\&=&\dfrac{481729333742972784}{193536000}\\
\end{eqnarray*}