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 \[\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\dfrac{-1}{0+\dfrac{127}{7}}\times\left(\left(-1\right)\times\left(-\dfrac{129}{11}\right)\times\left(-\dfrac{113}{4}\right)\times\left(-\dfrac{7}{2}\right)-\dfrac{95}{4}-\dfrac{103}{11}\right)\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}-\left(\dfrac{\dfrac{\dfrac{-1}{0}}{\dfrac{29}{3}}}{0}-\dfrac{127}{7}\times\dfrac{29}{3}\right)-10-\left(\dfrac{29}{3}+\dfrac{6}{5}+\dfrac{\dfrac{-\dfrac{7}{2}}{-1}}{-\dfrac{7}{2}}+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\dfrac{-1}{0+\dfrac{127}{7}}\times\left(\left(-1\right)\times\left(-\dfrac{129}{11}\right)\times\left(-\dfrac{113}{4}\right)\times\left(-\dfrac{7}{2}\right)-\dfrac{95}{4}-\dfrac{103}{11}\right)\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}-\left(\dfrac{\dfrac{\dfrac{-1}{0}}{\dfrac{29}{3}}}{0}-\dfrac{127}{7}\times\dfrac{29}{3}\right)-10-\left(\dfrac{29}{3}+\dfrac{6}{5}+\dfrac{\dfrac{-\dfrac{7}{2}}{-1}}{-\dfrac{7}{2}}+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}=-\dfrac{103102886250}{2151380}$ . Voici le détail : \begin{eqnarray*} X &=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\dfrac{-1}{\dfrac{127}{7}}\times\left(\left(-1\right)\times\left(-\dfrac{129}{11}\right)\times\left(-\dfrac{113}{4}\right)\times\left(-\dfrac{7}{2}\right)-\dfrac{95}{4}-\dfrac{103}{11}\right)\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}-\left(\dfrac{\dfrac{\dfrac{-1}{0}}{\dfrac{29}{3}}}{0}-\dfrac{127}{7}\times\dfrac{29}{3}\right)-10-\left(\dfrac{29}{3}+\dfrac{6}{5}+\dfrac{\dfrac{-\dfrac{7}{2}}{-1}}{-\dfrac{7}{2}}+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\dfrac{-1}{\dfrac{127}{7}}\times\left(\dfrac{129}{11}\times\left(-\dfrac{113}{4}\right)\times\left(-\dfrac{7}{2}\right)-\dfrac{95}{4}-\dfrac{103}{11}\right)\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}-\left(\dfrac{\dfrac{\dfrac{-1}{0}}{\dfrac{29}{3}}}{0}-\dfrac{127}{7}\times\dfrac{29}{3}\right)-10-\left(\dfrac{29}{3}+\dfrac{6}{5}+\dfrac{\dfrac{-\dfrac{7}{2}}{-1}}{-\dfrac{7}{2}}+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\dfrac{-1}{\dfrac{127}{7}}\times\left(\left(-\dfrac{14577}{44}\right)\times\left(-\dfrac{7}{2}\right)-\dfrac{95}{4}-\dfrac{103}{11}\right)\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}-\left(\dfrac{\dfrac{\dfrac{-1}{0}}{\dfrac{29}{3}}}{0}-\dfrac{127}{7}\times\dfrac{29}{3}\right)-10-\left(\dfrac{29}{3}+\dfrac{6}{5}+\dfrac{\dfrac{-\dfrac{7}{2}}{-1}}{-\dfrac{7}{2}}+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\dfrac{-1}{\dfrac{127}{7}}\times\left(\dfrac{102039}{88}-\dfrac{95}{4}-\dfrac{103}{11}\right)\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}-\left(\dfrac{\dfrac{\dfrac{-1}{0}}{\dfrac{29}{3}}}{0}-\dfrac{127}{7}\times\dfrac{29}{3}\right)-10-\left(\dfrac{29}{3}+\dfrac{6}{5}+\dfrac{\dfrac{-\dfrac{7}{2}}{-1}}{-\dfrac{7}{2}}+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\dfrac{-1}{\dfrac{127}{7}}\times\left(\dfrac{102039}{88}-\dfrac{95}{4}-\dfrac{103}{11}\right)\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}-\left(\dfrac{\dfrac{0}{\dfrac{29}{3}}}{0}-\dfrac{127}{7}\times\dfrac{29}{3}\right)-10-\left(\dfrac{29}{3}+\dfrac{6}{5}+\dfrac{\dfrac{-\dfrac{7}{2}}{-1}}{-\dfrac{7}{2}}+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\dfrac{-1}{\dfrac{127}{7}}\times\left(\dfrac{102039}{88}-\dfrac{95}{4}-\dfrac{103}{11}\right)\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}-\left(\dfrac{0}{0}-\dfrac{127}{7}\times\dfrac{29}{3}\right)-10-\left(\dfrac{29}{3}+\dfrac{6}{5}+\dfrac{\dfrac{-\dfrac{7}{2}}{-1}}{-\dfrac{7}{2}}+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\dfrac{-1}{\dfrac{127}{7}}\times\left(\dfrac{102039}{88}-\dfrac{95}{4}-\dfrac{103}{11}\right)\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}-\left(0-\dfrac{127}{7}\times\dfrac{29}{3}\right)-10-\left(\dfrac{29}{3}+\dfrac{6}{5}+\dfrac{\dfrac{-\dfrac{7}{2}}{-1}}{-\dfrac{7}{2}}+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\dfrac{-1}{\dfrac{127}{7}}\times\left(\dfrac{102039}{88}-\dfrac{95}{4}-\dfrac{103}{11}\right)\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}-\left(0-\dfrac{3683}{21}\right)-10-\left(\dfrac{29}{3}+\dfrac{6}{5}+\dfrac{\dfrac{-\dfrac{7}{2}}{-1}}{-\dfrac{7}{2}}+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\dfrac{-1}{\dfrac{127}{7}}\times\left(\dfrac{102039}{88}-\dfrac{95}{4}-\dfrac{103}{11}\right)\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}-\left(0-\dfrac{3683}{21}\right)-10-\left(\dfrac{29}{3}+\dfrac{6}{5}+\dfrac{\dfrac{7}{2}}{-\dfrac{7}{2}}+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\dfrac{-1}{\dfrac{127}{7}}\times\left(\dfrac{102039}{88}-\dfrac{95}{4}-\dfrac{103}{11}\right)\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}-\left(0-\dfrac{3683}{21}\right)-10-\left(\dfrac{29}{3}+\dfrac{6}{5}-1+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\left(-\dfrac{7}{127}\right)\times\left(\dfrac{102039}{88}-\dfrac{95}{4}-\dfrac{103}{11}\right)\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}-\left(0-\dfrac{3683}{21}\right)-10-\left(\dfrac{29}{3}+\dfrac{6}{5}-1+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\left(-\dfrac{7}{127}\right)\times\left(\dfrac{99949}{88}-\dfrac{103}{11}\right)\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}-\left(0-\dfrac{3683}{21}\right)-10-\left(\dfrac{29}{3}+\dfrac{6}{5}-1+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\left(-\dfrac{7}{127}\right)\times\dfrac{99125}{88}\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}-\left(0-\dfrac{3683}{21}\right)-10-\left(\dfrac{29}{3}+\dfrac{6}{5}-1+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\left(-\dfrac{7}{127}\right)\times\dfrac{99125}{88}\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}+\dfrac{3683}{21}-10-\left(\dfrac{29}{3}+\dfrac{6}{5}-1+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\left(-\dfrac{7}{127}\right)\times\dfrac{99125}{88}\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}+\dfrac{3683}{21}-10-\left(\dfrac{163}{15}-1+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\left(-\dfrac{7}{127}\right)\times\dfrac{99125}{88}\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}+\dfrac{3683}{21}-10-\left(\dfrac{148}{15}+\dfrac{39}{11}\right)}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\left(-\dfrac{7}{127}\right)\times\dfrac{99125}{88}\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}+\dfrac{3683}{21}-10-\dfrac{2213}{165}}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\left(-\dfrac{693875}{11176}\right)\times10+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}+\dfrac{3683}{21}-10-\dfrac{2213}{165}}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\left(-\dfrac{3469375}{5588}\right)+\dfrac{\dfrac{\dfrac{0}{\dfrac{29}{3}+\dfrac{3683}{21}-10-\dfrac{2213}{165}}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\left(-\dfrac{3469375}{5588}\right)+\dfrac{\dfrac{\dfrac{0}{\dfrac{3886}{21}-10-\dfrac{2213}{165}}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\left(-\dfrac{3469375}{5588}\right)+\dfrac{\dfrac{\dfrac{0}{\dfrac{3676}{21}-\dfrac{2213}{165}}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\left(-\dfrac{3469375}{5588}\right)+\dfrac{\dfrac{\dfrac{0}{\dfrac{186689}{1155}}}{-\dfrac{19}{3}+0}}{-11}\\&=&\dfrac{127}{7}\times\dfrac{39}{11}\times\dfrac{6}{5}\times\left(-\dfrac{3469375}{5588}\right)+\dfrac{\dfrac{\dfrac{0}{\dfrac{186689}{1155}}}{-\dfrac{19}{3}}}{-11}\\&=&\dfrac{4953}{77}\times\dfrac{6}{5}\times\left(-\dfrac{3469375}{5588}\right)+\dfrac{\dfrac{\dfrac{0}{\dfrac{186689}{1155}}}{-\dfrac{19}{3}}}{-11}\\&=&\dfrac{29718}{385}\times\left(-\dfrac{3469375}{5588}\right)+\dfrac{\dfrac{\dfrac{0}{\dfrac{186689}{1155}}}{-\dfrac{19}{3}}}{-11}\\&=&-\dfrac{103102886250}{2151380}+\dfrac{\dfrac{\dfrac{0}{\dfrac{186689}{1155}}}{-\dfrac{19}{3}}}{-11}\\&=&-\dfrac{103102886250}{2151380}+\dfrac{\dfrac{0}{-\dfrac{19}{3}}}{-11}\\&=&-\dfrac{103102886250}{2151380}+\dfrac{0}{-11}\\&=&-\dfrac{103102886250}{2151380}+0\\&=&-\dfrac{103102886250}{2151380}\\ \end{eqnarray*}