Ataraxy

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Exercice

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 \[\left(\left(0-\dfrac{45}{2}+0\times\dfrac{97}{9}\times\left(-1\right)-2\right)\times\left(-1\right)\times\dfrac{118}{9}\times\dfrac{\dfrac{-1}{-\dfrac{131}{12}}}{\dfrac{45}{2}}\times\left(0-\left(\dfrac{45}{2}+2\right)\right)-11\right)\times\left(12+\left(-1-\dfrac{97}{9}\right)-\left(-\dfrac{7}{8}-2\right)+12+\dfrac{\dfrac{45}{2}+5}{\dfrac{97}{9}+0}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=\left(\left(0-\dfrac{45}{2}+0\times\dfrac{97}{9}\times\left(-1\right)-2\right)\times\left(-1\right)\times\dfrac{118}{9}\times\dfrac{\dfrac{-1}{-\dfrac{131}{12}}}{\dfrac{45}{2}}\times\left(0-\left(\dfrac{45}{2}+2\right)\right)-11\right)\times\left(12+\left(-1-\dfrac{97}{9}\right)-\left(-\dfrac{7}{8}-2\right)+12+\dfrac{\dfrac{45}{2}+5}{\dfrac{97}{9}+0}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)=-\dfrac{2487923188537}{2840776920}$ . Voici le détail : \begin{eqnarray*} X &=&\left(\left(-\dfrac{45}{2}+0\times\dfrac{97}{9}\times\left(-1\right)-2\right)\times\left(-1\right)\times\dfrac{118}{9}\times\dfrac{\dfrac{-1}{-\dfrac{131}{12}}}{\dfrac{45}{2}}\times\left(0-\left(\dfrac{45}{2}+2\right)\right)-11\right)\times\left(12+\left(-1-\dfrac{97}{9}\right)-\left(-\dfrac{7}{8}-2\right)+12+\dfrac{\dfrac{45}{2}+5}{\dfrac{97}{9}+0}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(\left(-\dfrac{45}{2}+0\times\left(-1\right)-2\right)\times\left(-1\right)\times\dfrac{118}{9}\times\dfrac{\dfrac{-1}{-\dfrac{131}{12}}}{\dfrac{45}{2}}\times\left(0-\left(\dfrac{45}{2}+2\right)\right)-11\right)\times\left(12+\left(-1-\dfrac{97}{9}\right)-\left(-\dfrac{7}{8}-2\right)+12+\dfrac{\dfrac{45}{2}+5}{\dfrac{97}{9}+0}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(\left(-\dfrac{45}{2}+0-2\right)\times\left(-1\right)\times\dfrac{118}{9}\times\dfrac{\dfrac{-1}{-\dfrac{131}{12}}}{\dfrac{45}{2}}\times\left(0-\left(\dfrac{45}{2}+2\right)\right)-11\right)\times\left(12+\left(-1-\dfrac{97}{9}\right)-\left(-\dfrac{7}{8}-2\right)+12+\dfrac{\dfrac{45}{2}+5}{\dfrac{97}{9}+0}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(\left(-\dfrac{45}{2}+0-2\right)\times\left(-1\right)\times\dfrac{118}{9}\times\dfrac{\dfrac{12}{131}}{\dfrac{45}{2}}\times\left(0-\left(\dfrac{45}{2}+2\right)\right)-11\right)\times\left(12+\left(-1-\dfrac{97}{9}\right)-\left(-\dfrac{7}{8}-2\right)+12+\dfrac{\dfrac{45}{2}+5}{\dfrac{97}{9}+0}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(\left(-\dfrac{45}{2}+0-2\right)\times\left(-1\right)\times\dfrac{118}{9}\times\dfrac{8}{1965}\times\left(0-\left(\dfrac{45}{2}+2\right)\right)-11\right)\times\left(12+\left(-1-\dfrac{97}{9}\right)-\left(-\dfrac{7}{8}-2\right)+12+\dfrac{\dfrac{45}{2}+5}{\dfrac{97}{9}+0}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(\left(-\dfrac{45}{2}+0-2\right)\times\left(-1\right)\times\dfrac{118}{9}\times\dfrac{8}{1965}\times\left(0-\dfrac{49}{2}\right)-11\right)\times\left(12+\left(-1-\dfrac{97}{9}\right)-\left(-\dfrac{7}{8}-2\right)+12+\dfrac{\dfrac{45}{2}+5}{\dfrac{97}{9}+0}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(\left(-\dfrac{45}{2}+0-2\right)\times\left(-1\right)\times\dfrac{118}{9}\times\dfrac{8}{1965}\times\left(0-\dfrac{49}{2}\right)-11\right)\times\left(12-\dfrac{106}{9}-\left(-\dfrac{7}{8}-2\right)+12+\dfrac{\dfrac{45}{2}+5}{\dfrac{97}{9}+0}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(\left(-\dfrac{45}{2}+0-2\right)\times\left(-1\right)\times\dfrac{118}{9}\times\dfrac{8}{1965}\times\left(0-\dfrac{49}{2}\right)-11\right)\times\left(12-\dfrac{106}{9}+\dfrac{23}{8}+12+\dfrac{\dfrac{45}{2}+5}{\dfrac{97}{9}+0}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(\left(-\dfrac{45}{2}+0-2\right)\times\left(-1\right)\times\dfrac{118}{9}\times\dfrac{8}{1965}\times\left(0-\dfrac{49}{2}\right)-11\right)\times\left(12-\dfrac{106}{9}+\dfrac{23}{8}+12+\dfrac{\dfrac{55}{2}}{\dfrac{97}{9}+0}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(\left(-\dfrac{45}{2}+0-2\right)\times\left(-1\right)\times\dfrac{118}{9}\times\dfrac{8}{1965}\times\left(0-\dfrac{49}{2}\right)-11\right)\times\left(12-\dfrac{106}{9}+\dfrac{23}{8}+12+\dfrac{\dfrac{55}{2}}{\dfrac{97}{9}}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(\left(-\dfrac{45}{2}+0-2\right)\times\left(-1\right)\times\dfrac{118}{9}\times\dfrac{8}{1965}\times\left(0-\dfrac{49}{2}\right)-11\right)\times\left(12-\dfrac{106}{9}+\dfrac{23}{8}+12+\dfrac{\dfrac{55}{2}}{\dfrac{97}{9}}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(\left(-\dfrac{45}{2}-2\right)\times\left(-1\right)\times\dfrac{118}{9}\times\dfrac{8}{1965}\times\left(0-\dfrac{49}{2}\right)-11\right)\times\left(12-\dfrac{106}{9}+\dfrac{23}{8}+12+\dfrac{\dfrac{55}{2}}{\dfrac{97}{9}}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(-\dfrac{49}{2}\times\left(-1\right)\times\dfrac{118}{9}\times\dfrac{8}{1965}\times\left(0-\dfrac{49}{2}\right)-11\right)\times\left(12-\dfrac{106}{9}+\dfrac{23}{8}+12+\dfrac{\dfrac{55}{2}}{\dfrac{97}{9}}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(-\dfrac{49}{2}\times\left(-\dfrac{118}{9}\right)\times\dfrac{8}{1965}\times\left(0-\dfrac{49}{2}\right)-11\right)\times\left(12-\dfrac{106}{9}+\dfrac{23}{8}+12+\dfrac{\dfrac{55}{2}}{\dfrac{97}{9}}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(-\dfrac{49}{2}\times\left(-\dfrac{944}{17685}\right)\times\left(0-\dfrac{49}{2}\right)-11\right)\times\left(12-\dfrac{106}{9}+\dfrac{23}{8}+12+\dfrac{\dfrac{55}{2}}{\dfrac{97}{9}}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(-\dfrac{49}{2}\times\left(-\dfrac{944}{17685}\right)\times-\dfrac{49}{2}-11\right)\times\left(12-\dfrac{106}{9}+\dfrac{23}{8}+12+\dfrac{\dfrac{55}{2}}{\dfrac{97}{9}}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(-\dfrac{49}{2}\times\left(-\dfrac{944}{17685}\right)\times-\dfrac{49}{2}-11\right)\times\left(12-\dfrac{641}{72}+12+\dfrac{\dfrac{55}{2}}{\dfrac{97}{9}}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(-\dfrac{49}{2}\times\left(-\dfrac{944}{17685}\right)\times-\dfrac{49}{2}-11\right)\times\left(12-\dfrac{641}{72}+12+\dfrac{495}{194}+\dfrac{\dfrac{5}{12}+12+0}{\dfrac{23}{5}}\right)\\&=&\left(-\dfrac{49}{2}\times\left(-\dfrac{944}{17685}\right)\times-\dfrac{49}{2}-11\right)\times\left(12-\dfrac{641}{72}+12+\dfrac{495}{194}+\dfrac{\dfrac{149}{12}+0}{\dfrac{23}{5}}\right)\\&=&\left(-\dfrac{49}{2}\times\left(-\dfrac{944}{17685}\right)\times-\dfrac{49}{2}-11\right)\times\left(12-\dfrac{641}{72}+12+\dfrac{495}{194}+\dfrac{\dfrac{149}{12}}{\dfrac{23}{5}}\right)\\&=&\left(\dfrac{23128}{17685}\times-\dfrac{49}{2}-11\right)\times\left(12-\dfrac{641}{72}+12+\dfrac{495}{194}+\dfrac{\dfrac{149}{12}}{\dfrac{23}{5}}\right)\\&=&\left(-\dfrac{566636}{17685}-11\right)\times\left(12-\dfrac{641}{72}+12+\dfrac{495}{194}+\dfrac{\dfrac{149}{12}}{\dfrac{23}{5}}\right)\\&=&\left(-\dfrac{566636}{17685}-11\right)\times\left(12+\dfrac{223}{72}+\dfrac{495}{194}+\dfrac{\dfrac{149}{12}}{\dfrac{23}{5}}\right)\\&=&\left(-\dfrac{566636}{17685}-11\right)\times\left(12+\dfrac{39451}{6984}+\dfrac{\dfrac{149}{12}}{\dfrac{23}{5}}\right)\\&=&\left(-\dfrac{566636}{17685}-11\right)\times\left(12+\dfrac{39451}{6984}+\dfrac{745}{276}\right)\\&=&-\dfrac{761171}{17685}\times\left(12+\dfrac{39451}{6984}+\dfrac{745}{276}\right)\\&=&-\dfrac{761171}{17685}\times\left(\dfrac{123259}{6984}+\dfrac{745}{276}\right)\\&=&-\dfrac{761171}{17685}\times\dfrac{3268547}{160632}\\&=&-\dfrac{2487923188537}{2840776920}\\ \end{eqnarray*}