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 \[\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\dfrac{5}{-11}\times\left(8+\dfrac{137}{5}-6\right)}{\left(-\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{33}{7}\right)\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6-\dfrac{\dfrac{9}{-\dfrac{17}{8}}}{5}-\left(2-5-\dfrac{51}{8}+11\right)+\dfrac{49}{5}+7-2+\dfrac{17}{8}-\dfrac{17}{8}+\dfrac{49}{5}-12+\dfrac{137}{5}+\dfrac{49}{5}\right)\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\dfrac{5}{-11}\times\left(8+\dfrac{137}{5}-6\right)}{\left(-\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{33}{7}\right)\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6-\dfrac{\dfrac{9}{-\dfrac{17}{8}}}{5}-\left(2-5-\dfrac{51}{8}+11\right)+\dfrac{49}{5}+7-2+\dfrac{17}{8}-\dfrac{17}{8}+\dfrac{49}{5}-12+\dfrac{137}{5}+\dfrac{49}{5}\right)=-\dfrac{156943987}{2715240}$ . Voici le détail : \begin{eqnarray*} X &=&\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\left(-\dfrac{5}{11}\right)\times\left(8+\dfrac{137}{5}-6\right)}{\left(-\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{33}{7}\right)\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6-\dfrac{\dfrac{9}{-\dfrac{17}{8}}}{5}-\left(2-5-\dfrac{51}{8}+11\right)+\dfrac{49}{5}+7-2+\dfrac{17}{8}-\dfrac{17}{8}+\dfrac{49}{5}-12+\dfrac{137}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\left(-\dfrac{5}{11}\right)\times\left(\dfrac{177}{5}-6\right)}{\left(-\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{33}{7}\right)\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6-\dfrac{\dfrac{9}{-\dfrac{17}{8}}}{5}-\left(2-5-\dfrac{51}{8}+11\right)+\dfrac{49}{5}+7-2+\dfrac{17}{8}-\dfrac{17}{8}+\dfrac{49}{5}-12+\dfrac{137}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\left(-\dfrac{5}{11}\right)\times\dfrac{147}{5}}{\left(-\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{33}{7}\right)\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6-\dfrac{\dfrac{9}{-\dfrac{17}{8}}}{5}-\left(2-5-\dfrac{51}{8}+11\right)+\dfrac{49}{5}+7-2+\dfrac{17}{8}-\dfrac{17}{8}+\dfrac{49}{5}-12+\dfrac{137}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\left(-\dfrac{5}{11}\right)\times\dfrac{147}{5}}{\left(0+\dfrac{33}{7}\right)\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6-\dfrac{\dfrac{9}{-\dfrac{17}{8}}}{5}-\left(2-5-\dfrac{51}{8}+11\right)+\dfrac{49}{5}+7-2+\dfrac{17}{8}-\dfrac{17}{8}+\dfrac{49}{5}-12+\dfrac{137}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\left(-\dfrac{5}{11}\right)\times\dfrac{147}{5}}{\dfrac{33}{7}\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6-\dfrac{\dfrac{9}{-\dfrac{17}{8}}}{5}-\left(2-5-\dfrac{51}{8}+11\right)+\dfrac{49}{5}+7-2+\dfrac{17}{8}-\dfrac{17}{8}+\dfrac{49}{5}-12+\dfrac{137}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\left(-\dfrac{5}{11}\right)\times\dfrac{147}{5}}{\dfrac{33}{7}\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6-\dfrac{-\dfrac{72}{17}}{5}-\left(2-5-\dfrac{51}{8}+11\right)+\dfrac{49}{5}+7-2+\dfrac{17}{8}-\dfrac{17}{8}+\dfrac{49}{5}-12+\dfrac{137}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\left(-\dfrac{5}{11}\right)\times\dfrac{147}{5}}{\dfrac{33}{7}\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6+\dfrac{72}{85}-\left(2-5-\dfrac{51}{8}+11\right)+\dfrac{49}{5}+7-2+\dfrac{17}{8}-\dfrac{17}{8}+\dfrac{49}{5}-12+\dfrac{137}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\left(-\dfrac{5}{11}\right)\times\dfrac{147}{5}}{\dfrac{33}{7}\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6+\dfrac{72}{85}-\left(-3-\dfrac{51}{8}+11\right)+\dfrac{49}{5}+7-2+\dfrac{17}{8}-\dfrac{17}{8}+\dfrac{49}{5}-12+\dfrac{137}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\left(-\dfrac{5}{11}\right)\times\dfrac{147}{5}}{\dfrac{33}{7}\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6+\dfrac{72}{85}-\left(-\dfrac{75}{8}+11\right)+\dfrac{49}{5}+7-2+\dfrac{17}{8}-\dfrac{17}{8}+\dfrac{49}{5}-12+\dfrac{137}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\left(-\dfrac{5}{11}\right)\times\dfrac{147}{5}}{\dfrac{33}{7}\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6+\dfrac{72}{85}-\dfrac{13}{8}+\dfrac{49}{5}+7-2+\dfrac{17}{8}-\dfrac{17}{8}+\dfrac{49}{5}-12+\dfrac{137}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\left(-\dfrac{5}{11}\right)\times\dfrac{147}{5}}{\dfrac{33}{7}\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6+\dfrac{72}{85}-\dfrac{13}{8}+\dfrac{84}{5}-2+\dfrac{17}{8}-\dfrac{17}{8}+\dfrac{49}{5}-12+\dfrac{137}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\left(-\dfrac{5}{11}\right)\times\dfrac{147}{5}}{\dfrac{33}{7}\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6+\dfrac{72}{85}-\dfrac{13}{8}+\dfrac{74}{5}+\dfrac{17}{8}-\dfrac{17}{8}+\dfrac{49}{5}-12+\dfrac{137}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\left(-\dfrac{5}{11}\right)\times\dfrac{147}{5}}{\dfrac{33}{7}\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6+\dfrac{72}{85}-\dfrac{13}{8}+\dfrac{677}{40}-\dfrac{17}{8}+\dfrac{49}{5}-12+\dfrac{137}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\left(-\dfrac{5}{11}\right)\times\dfrac{147}{5}}{\dfrac{33}{7}\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6+\dfrac{72}{85}-\dfrac{13}{8}+\dfrac{677}{40}-\dfrac{17}{8}-\dfrac{11}{5}+\dfrac{137}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{\dfrac{49}{5}\times\left(-\dfrac{5}{11}\right)\times\dfrac{147}{5}}{\dfrac{33}{7}\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6+\dfrac{72}{85}-\dfrac{13}{8}+\dfrac{677}{40}-\dfrac{17}{8}+\dfrac{126}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{\left(-\dfrac{49}{11}\right)\times\dfrac{147}{5}}{\dfrac{33}{7}\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6+\dfrac{72}{85}-\dfrac{13}{8}+\dfrac{677}{40}-\dfrac{17}{8}+\dfrac{126}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{-\dfrac{7203}{55}}{\dfrac{33}{7}\times6\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6+\dfrac{72}{85}-\dfrac{13}{8}+\dfrac{677}{40}-\dfrac{17}{8}+\dfrac{126}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{-\dfrac{7203}{55}}{\dfrac{198}{7}\times\left(-11\right)}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6+\dfrac{72}{85}-\dfrac{13}{8}+\dfrac{677}{40}-\dfrac{17}{8}+\dfrac{126}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{-\dfrac{7203}{55}}{-\dfrac{2178}{7}}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+6+\dfrac{72}{85}-\dfrac{13}{8}+\dfrac{677}{40}-\dfrac{17}{8}+\dfrac{126}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{-\dfrac{7203}{55}}{-\dfrac{2178}{7}}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+\dfrac{582}{85}-\dfrac{13}{8}+\dfrac{677}{40}-\dfrac{17}{8}+\dfrac{126}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{-\dfrac{7203}{55}}{-\dfrac{2178}{7}}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+\dfrac{3551}{680}+\dfrac{677}{40}-\dfrac{17}{8}+\dfrac{126}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{-\dfrac{7203}{55}}{-\dfrac{2178}{7}}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+\dfrac{3551}{680}+\dfrac{74}{5}+\dfrac{126}{5}+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{-\dfrac{7203}{55}}{-\dfrac{2178}{7}}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+\dfrac{3551}{680}+40+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{16807}{39930}+\dfrac{49}{5}\right)-\left(2-\dfrac{1}{2}+\dfrac{3551}{680}+40+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{16807}{39930}+\dfrac{49}{5}\right)-\left(\dfrac{3}{2}+\dfrac{3551}{680}+40+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{16807}{39930}+\dfrac{49}{5}\right)-\left(\dfrac{4571}{680}+40+\dfrac{49}{5}\right)\\&=&\left(-11-\dfrac{1}{2}+\dfrac{16807}{39930}+\dfrac{49}{5}\right)-\left(\dfrac{31771}{680}+\dfrac{49}{5}\right)\\&=&\left(-\dfrac{23}{2}+\dfrac{16807}{39930}+\dfrac{49}{5}\right)-\left(\dfrac{31771}{680}+\dfrac{49}{5}\right)\\&=&\left(-\dfrac{221194}{19965}+\dfrac{49}{5}\right)-\left(\dfrac{31771}{680}+\dfrac{49}{5}\right)\\&=&-\dfrac{25537}{19965}-\left(\dfrac{31771}{680}+\dfrac{49}{5}\right)\\&=&-\dfrac{25537}{19965}-\dfrac{7687}{136}\\&=&-\dfrac{156943987}{2715240}\\ \end{eqnarray*}