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 \[\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-4\right)\times\left(-\dfrac{94}{5}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{1}{2}}{\left(-2\right)\times\left(-11\right)\times\left(-3\right)\times\left(-\dfrac{34}{5}\right)}}{\dfrac{62}{3}}}{11}\times\left(\dfrac{-\dfrac{1}{2}}{-12}-\dfrac{1}{2}+12-\dfrac{94}{5}-3-\dfrac{1}{2}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{11\times12}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-4\right)\times\left(-\dfrac{94}{5}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{1}{2}}{\left(-2\right)\times\left(-11\right)\times\left(-3\right)\times\left(-\dfrac{34}{5}\right)}}{\dfrac{62}{3}}}{11}\times\left(\dfrac{-\dfrac{1}{2}}{-12}-\dfrac{1}{2}+12-\dfrac{94}{5}-3-\dfrac{1}{2}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{11\times12}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}=-\dfrac{60070230}{3182612822079356160}$ . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-4\right)\times\left(-\dfrac{94}{5}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{1}{2}}{22\times\left(-3\right)\times\left(-\dfrac{34}{5}\right)}}{\dfrac{62}{3}}}{11}\times\left(\dfrac{-\dfrac{1}{2}}{-12}-\dfrac{1}{2}+12-\dfrac{94}{5}-3-\dfrac{1}{2}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{11\times12}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-4\right)\times\left(-\dfrac{94}{5}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{1}{2}}{\left(-66\right)\times\left(-\dfrac{34}{5}\right)}}{\dfrac{62}{3}}}{11}\times\left(\dfrac{-\dfrac{1}{2}}{-12}-\dfrac{1}{2}+12-\dfrac{94}{5}-3-\dfrac{1}{2}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{11\times12}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-4\right)\times\left(-\dfrac{94}{5}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{1}{2}}{\dfrac{2244}{5}}}{\dfrac{62}{3}}}{11}\times\left(\dfrac{-\dfrac{1}{2}}{-12}-\dfrac{1}{2}+12-\dfrac{94}{5}-3-\dfrac{1}{2}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{11\times12}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-4\right)\times\left(-\dfrac{94}{5}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{1}{2}}{\dfrac{2244}{5}}}{\dfrac{62}{3}}}{11}\times\left(\dfrac{1}{24}-\dfrac{1}{2}+12-\dfrac{94}{5}-3-\dfrac{1}{2}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{11\times12}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-4\right)\times\left(-\dfrac{94}{5}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{1}{2}}{\dfrac{2244}{5}}}{\dfrac{62}{3}}}{11}\times\left(\dfrac{1}{24}-\dfrac{1}{2}+12-\dfrac{109}{5}-\dfrac{1}{2}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{11\times12}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-4\right)\times\left(-\dfrac{94}{5}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{1}{2}}{\dfrac{2244}{5}}}{\dfrac{62}{3}}}{11}\times\left(\dfrac{1}{24}-\dfrac{1}{2}+12-\dfrac{223}{10}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{11\times12}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-4\right)\times\left(-\dfrac{94}{5}\right)\times\dfrac{\dfrac{-\dfrac{5}{4488}}{\dfrac{62}{3}}}{11}\times\left(\dfrac{1}{24}-\dfrac{1}{2}+12-\dfrac{223}{10}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{11\times12}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-4\right)\times\left(-\dfrac{94}{5}\right)\times\dfrac{-\dfrac{5}{92752}}{11}\times\left(\dfrac{1}{24}-\dfrac{1}{2}+12-\dfrac{223}{10}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{11\times12}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-4\right)\times\left(-\dfrac{94}{5}\right)\times\left(-\dfrac{5}{1020272}\right)\times\left(\dfrac{1}{24}-\dfrac{1}{2}+12-\dfrac{223}{10}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{11\times12}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-4\right)\times\left(-\dfrac{94}{5}\right)\times\left(-\dfrac{5}{1020272}\right)\times\left(-\dfrac{11}{24}+12-\dfrac{223}{10}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{11\times12}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-4\right)\times\left(-\dfrac{94}{5}\right)\times\left(-\dfrac{5}{1020272}\right)\times\left(\dfrac{277}{24}-\dfrac{223}{10}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{11\times12}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-4\right)\times\left(-\dfrac{94}{5}\right)\times\left(-\dfrac{5}{1020272}\right)\times\left(-\dfrac{1291}{120}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{11\times12}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-4\right)\times\left(-\dfrac{94}{5}\right)\times\left(-\dfrac{5}{1020272}\right)\times\left(-\dfrac{1291}{120}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{132}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{376}{5}\times\left(-\dfrac{5}{1020272}\right)\times\left(-\dfrac{1291}{120}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{132}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\left(-\dfrac{47}{127534}\right)\times\left(-\dfrac{1291}{120}\right)}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{132}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{60677}{15304080}}{-3}}{\left(-11\right)\times12}}{11}}{-11+\dfrac{\dfrac{62}{3}}{132}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{60677}{15304080}}{-3}}{-132}}{11}}{-11+\dfrac{\dfrac{62}{3}}{132}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{60677}{15304080}}{-3}}{-132}}{11}}{-11+\dfrac{31}{198}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{60677}{45912240}}{-132}}{11}}{-11+\dfrac{31}{198}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{60677}{6060415680}}{11}}{-11+\dfrac{31}{198}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{60677}{6060415680}}{11}}{-\dfrac{2147}{198}}}{\left(-2\right)\times\left(-\dfrac{34}{5}\right)\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{60677}{6060415680}}{11}}{-\dfrac{2147}{198}}}{\dfrac{68}{5}\times12\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{60677}{6060415680}}{11}}{-\dfrac{2147}{198}}}{\dfrac{816}{5}\times\dfrac{109}{4}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{60677}{6060415680}}{11}}{-\dfrac{2147}{198}}}{\dfrac{22236}{5}}\\&=&\dfrac{\dfrac{\dfrac{60677}{66664572480}}{-\dfrac{2147}{198}}}{\dfrac{22236}{5}}\\&=&\dfrac{-\dfrac{12014046}{143128837114560}}{\dfrac{22236}{5}}\\&=&-\dfrac{60070230}{3182612822079356160}\\ \end{eqnarray*}