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 \[\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{\dfrac{5}{-4}}}{-4}}{10}}}{4-\left(11-\left(-4+\dfrac{29}{4}-5-\dfrac{95}{11}\right)\times\dfrac{95}{11}\times1-\left(\dfrac{38}{9}-4-10+1\right)\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times\left(1+11\right)\times\left(\dfrac{\dfrac{7}{\dfrac{95}{11}}}{-\dfrac{17}{2}}+5+4\right)\times\left(-\dfrac{29}{4}\right)\times3}\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{\dfrac{5}{-4}}}{-4}}{10}}}{4-\left(11-\left(-4+\dfrac{29}{4}-5-\dfrac{95}{11}\right)\times\dfrac{95}{11}\times1-\left(\dfrac{38}{9}-4-10+1\right)\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times\left(1+11\right)\times\left(\dfrac{\dfrac{7}{\dfrac{95}{11}}}{-\dfrac{17}{2}}+5+4\right)\times\left(-\dfrac{29}{4}\right)\times3}=\dfrac{1279080000}{54016381241883}$ . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{\dfrac{5}{-4}}}{-4}}{10}}}{4-\left(11-\left(\dfrac{13}{4}-5-\dfrac{95}{11}\right)\times\dfrac{95}{11}\times1-\left(\dfrac{38}{9}-4-10+1\right)\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times\left(1+11\right)\times\left(\dfrac{\dfrac{7}{\dfrac{95}{11}}}{-\dfrac{17}{2}}+5+4\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{\dfrac{5}{-4}}}{-4}}{10}}}{4-\left(11-\left(-\dfrac{7}{4}-\dfrac{95}{11}\right)\times\dfrac{95}{11}\times1-\left(\dfrac{38}{9}-4-10+1\right)\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times\left(1+11\right)\times\left(\dfrac{\dfrac{7}{\dfrac{95}{11}}}{-\dfrac{17}{2}}+5+4\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{\dfrac{5}{-4}}}{-4}}{10}}}{4-\left(11+\dfrac{457}{44}\times\dfrac{95}{11}\times1-\left(\dfrac{38}{9}-4-10+1\right)\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times\left(1+11\right)\times\left(\dfrac{\dfrac{7}{\dfrac{95}{11}}}{-\dfrac{17}{2}}+5+4\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{\dfrac{5}{-4}}}{-4}}{10}}}{4-\left(11+\dfrac{457}{44}\times\dfrac{95}{11}\times1-\left(\dfrac{38}{9}-4-10+1\right)\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times\left(1+11\right)\times\left(\dfrac{\dfrac{77}{95}}{-\dfrac{17}{2}}+5+4\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{\dfrac{5}{-4}}}{-4}}{10}}}{4-\left(11+\dfrac{457}{44}\times\dfrac{95}{11}\times1-\left(\dfrac{38}{9}-4-10+1\right)\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times\left(1+11\right)\times\left(-\dfrac{154}{1615}+5+4\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{\dfrac{5}{-4}}}{-4}}{10}}}{4-\left(11+\dfrac{43415}{484}\times1-\left(\dfrac{38}{9}-4-10+1\right)\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times\left(1+11\right)\times\left(-\dfrac{154}{1615}+5+4\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{\dfrac{5}{-4}}}{-4}}{10}}}{4-\left(11+\dfrac{43415}{484}-\left(\dfrac{38}{9}-4-10+1\right)\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times\left(1+11\right)\times\left(-\dfrac{154}{1615}+5+4\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{\dfrac{5}{-4}}}{-4}}{10}}}{4-\left(11+\dfrac{43415}{484}-\left(\dfrac{2}{9}-10+1\right)\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times\left(1+11\right)\times\left(-\dfrac{154}{1615}+5+4\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{\dfrac{5}{-4}}}{-4}}{10}}}{4-\left(11+\dfrac{43415}{484}-\left(-\dfrac{88}{9}+1\right)\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times\left(1+11\right)\times\left(-\dfrac{154}{1615}+5+4\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{\dfrac{5}{-4}}}{-4}}{10}}}{4-\left(11+\dfrac{43415}{484}+\dfrac{79}{9}\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times\left(1+11\right)\times\left(-\dfrac{154}{1615}+5+4\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{\dfrac{5}{-4}}}{-4}}{10}}}{4-\left(11+\dfrac{43415}{484}+\dfrac{79}{9}\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times12\times\left(-\dfrac{154}{1615}+5+4\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{\dfrac{5}{-4}}}{-4}}{10}}}{4-\left(11+\dfrac{43415}{484}+\dfrac{79}{9}\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times12\times\left(\dfrac{7921}{1615}+4\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{\dfrac{5}{-4}}}{-4}}{10}}}{4-\left(11+\dfrac{43415}{484}+\dfrac{79}{9}\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times12\times\dfrac{14381}{1615}\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{5}{4}}}{-4}}{10}}}{4-\left(11+\dfrac{43415}{484}+\dfrac{79}{9}\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times12\times\dfrac{14381}{1615}\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{5}{4}}}{-4}}{10}}}{4-\left(\dfrac{48739}{484}+\dfrac{79}{9}\right)-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times12\times\dfrac{14381}{1615}\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{5}{4}}}{-4}}{10}}}{4-\dfrac{476887}{4356}-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{29}{4}\right)\times12\times\dfrac{14381}{1615}\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{5}{4}}}{-4}}{10}}}{4-\dfrac{476887}{4356}-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-87\right)\times\dfrac{14381}{1615}\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{\dfrac{11}{-\dfrac{5}{4}}}{-4}}{10}}}{4-\dfrac{476887}{4356}-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{1251147}{1615}\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{-\dfrac{44}{5}}{-4}}{10}}}{4-\dfrac{476887}{4356}-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{1251147}{1615}\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{\dfrac{11}{5}}{10}}}{4-\dfrac{476887}{4356}-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{1251147}{1615}\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{11}{50}}}{4-\dfrac{476887}{4356}-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{1251147}{1615}\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{11}{50}}}{-\dfrac{459463}{4356}-\dfrac{38}{9}-\dfrac{38}{9}}}{\left(-\dfrac{1251147}{1615}\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{11}{50}}}{-\dfrac{53095}{484}-\dfrac{38}{9}}}{\left(-\dfrac{1251147}{1615}\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{11}{50}}}{-\dfrac{496247}{4356}}}{\left(-\dfrac{1251147}{1615}\right)\times\left(-\dfrac{29}{4}\right)\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{11}{50}}}{-\dfrac{496247}{4356}}}{\dfrac{36283263}{6460}\times3}\\&=&\dfrac{\dfrac{\dfrac{-10}{\dfrac{11}{50}}}{-\dfrac{496247}{4356}}}{\dfrac{108849789}{6460}}\\&=&\dfrac{\dfrac{-\dfrac{500}{11}}{-\dfrac{496247}{4356}}}{\dfrac{108849789}{6460}}\\&=&\dfrac{\dfrac{198000}{496247}}{\dfrac{108849789}{6460}}\\&=&\dfrac{1279080000}{54016381241883}\\ \end{eqnarray*}