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 \[\dfrac{\dfrac{\dfrac{\left(\dfrac{\dfrac{\dfrac{-5}{-\dfrac{93}{10}}}{-10}}{-\dfrac{136}{3}}+\dfrac{\dfrac{-\dfrac{29}{2}}{6}}{-5}-4+\dfrac{25}{7}+\dfrac{47}{2}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{47}{2}}{-\dfrac{92}{7}}}{\dfrac{128}{9}}}{-\dfrac{92}{7}-\dfrac{93}{10}-\dfrac{93}{10}-\dfrac{11}{4}}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=\dfrac{\dfrac{\dfrac{\left(\dfrac{\dfrac{\dfrac{-5}{-\dfrac{93}{10}}}{-10}}{-\dfrac{136}{3}}+\dfrac{\dfrac{-\dfrac{29}{2}}{6}}{-5}-4+\dfrac{25}{7}+\dfrac{47}{2}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{47}{2}}{-\dfrac{92}{7}}}{\dfrac{128}{9}}}{-\dfrac{92}{7}-\dfrac{93}{10}-\dfrac{93}{10}-\dfrac{11}{4}}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}=-\dfrac{88924489536960000}{2.0859579829045E+21}$ . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{\dfrac{\left(\dfrac{\dfrac{\dfrac{50}{93}}{-10}}{-\dfrac{136}{3}}+\dfrac{\dfrac{-\dfrac{29}{2}}{6}}{-5}-4+\dfrac{25}{7}+\dfrac{47}{2}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{47}{2}}{-\dfrac{92}{7}}}{\dfrac{128}{9}}}{-\dfrac{92}{7}-\dfrac{93}{10}-\dfrac{93}{10}-\dfrac{11}{4}}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\left(\dfrac{-\dfrac{5}{93}}{-\dfrac{136}{3}}+\dfrac{\dfrac{-\dfrac{29}{2}}{6}}{-5}-4+\dfrac{25}{7}+\dfrac{47}{2}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{47}{2}}{-\dfrac{92}{7}}}{\dfrac{128}{9}}}{-\dfrac{92}{7}-\dfrac{93}{10}-\dfrac{93}{10}-\dfrac{11}{4}}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\left(\dfrac{5}{4216}+\dfrac{\dfrac{-\dfrac{29}{2}}{6}}{-5}-4+\dfrac{25}{7}+\dfrac{47}{2}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{47}{2}}{-\dfrac{92}{7}}}{\dfrac{128}{9}}}{-\dfrac{92}{7}-\dfrac{93}{10}-\dfrac{93}{10}-\dfrac{11}{4}}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\left(\dfrac{5}{4216}+\dfrac{-\dfrac{29}{12}}{-5}-4+\dfrac{25}{7}+\dfrac{47}{2}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{47}{2}}{-\dfrac{92}{7}}}{\dfrac{128}{9}}}{-\dfrac{92}{7}-\dfrac{93}{10}-\dfrac{93}{10}-\dfrac{11}{4}}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\left(\dfrac{5}{4216}+\dfrac{29}{60}-4+\dfrac{25}{7}+\dfrac{47}{2}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{47}{2}}{-\dfrac{92}{7}}}{\dfrac{128}{9}}}{-\dfrac{92}{7}-\dfrac{93}{10}-\dfrac{93}{10}-\dfrac{11}{4}}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\left(\dfrac{5}{4216}+\dfrac{29}{60}-4+\dfrac{25}{7}+\dfrac{47}{2}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{47}{2}}{-\dfrac{92}{7}}}{\dfrac{128}{9}}}{-\dfrac{1571}{70}-\dfrac{93}{10}-\dfrac{11}{4}}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\left(\dfrac{5}{4216}+\dfrac{29}{60}-4+\dfrac{25}{7}+\dfrac{47}{2}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{47}{2}}{-\dfrac{92}{7}}}{\dfrac{128}{9}}}{-\dfrac{1111}{35}-\dfrac{11}{4}}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\left(\dfrac{5}{4216}+\dfrac{29}{60}-4+\dfrac{25}{7}+\dfrac{47}{2}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{47}{2}}{-\dfrac{92}{7}}}{\dfrac{128}{9}}}{-\dfrac{4829}{140}}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\left(\dfrac{30641}{63240}-4+\dfrac{25}{7}+\dfrac{47}{2}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{47}{2}}{-\dfrac{92}{7}}}{\dfrac{128}{9}}}{-\dfrac{4829}{140}}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\left(-\dfrac{222319}{63240}+\dfrac{25}{7}+\dfrac{47}{2}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{47}{2}}{-\dfrac{92}{7}}}{\dfrac{128}{9}}}{-\dfrac{4829}{140}}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\left(-\dfrac{222319}{63240}+\dfrac{25}{7}+\dfrac{47}{2}\right)\times\dfrac{\dfrac{-\dfrac{329}{184}}{\dfrac{128}{9}}}{-\dfrac{4829}{140}}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\left(-\dfrac{222319}{63240}+\dfrac{25}{7}+\dfrac{47}{2}\right)\times\dfrac{-\dfrac{2961}{23552}}{-\dfrac{4829}{140}}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\left(-\dfrac{222319}{63240}+\dfrac{25}{7}+\dfrac{47}{2}\right)\times\dfrac{103635}{28433152}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\left(\dfrac{24767}{442680}+\dfrac{47}{2}\right)\times\dfrac{103635}{28433152}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{10427747}{442680}\times\dfrac{103635}{28433152}\times\dfrac{25}{7}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{10427747}{442680}\times\dfrac{370125}{28433152}\times\dfrac{\dfrac{\dfrac{128}{9}}{-4}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{10427747}{442680}\times\dfrac{370125}{28433152}\times\dfrac{-\dfrac{32}{9}}{-\dfrac{45}{2}}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{10427747}{442680}\times\dfrac{370125}{28433152}\times\dfrac{64}{405}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{3859569858375}{12586787727360}\times\dfrac{64}{405}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{247012470936000}{5097649029580800}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\left(-5\right)\times\left(-\dfrac{11}{4}\right)}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{247012470936000}{5097649029580800}}{\dfrac{80}{9}}}{-\dfrac{93}{10}}}{\dfrac{55}{4}}\\&=&\dfrac{\dfrac{\dfrac{2223112238424000}{407811922366464000}}{-\dfrac{93}{10}}}{\dfrac{55}{4}}\\&=&\dfrac{-\dfrac{22231122384240000}{3.7926508780081E+19}}{\dfrac{55}{4}}\\&=&-\dfrac{88924489536960000}{2.0859579829045E+21}\\ \end{eqnarray*}