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 \[-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-6\right)\times8\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{101}{12}\right)\times\dfrac{4}{11}\times\dfrac{114}{7}\times3\times\left(-\dfrac{109}{12}\right)\times\dfrac{7}{5}\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(\left(-\dfrac{117}{7}\right)\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{2}{7}\right)+\left(-\dfrac{40}{3}\right)\times8\times\left(-\dfrac{55}{7}\right)\times8-\dfrac{40}{3}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-6\right)\times8\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{101}{12}\right)\times\dfrac{4}{11}\times\dfrac{114}{7}\times3\times\left(-\dfrac{109}{12}\right)\times\dfrac{7}{5}\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(\left(-\dfrac{117}{7}\right)\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{2}{7}\right)+\left(-\dfrac{40}{3}\right)\times8\times\left(-\dfrac{55}{7}\right)\times8-\dfrac{40}{3}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)=-\dfrac{44172787244089735}{452948650}$ . Voici le détail : \begin{eqnarray*} X &=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-6\right)\times8\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{101}{12}\right)\times\dfrac{456}{77}\times3\times\left(-\dfrac{109}{12}\right)\times\dfrac{7}{5}\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(\left(-\dfrac{117}{7}\right)\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{2}{7}\right)+\left(-\dfrac{40}{3}\right)\times8\times\left(-\dfrac{55}{7}\right)\times8-\dfrac{40}{3}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-6\right)\times8\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{101}{12}\right)\times\dfrac{1368}{77}\times\left(-\dfrac{109}{12}\right)\times\dfrac{7}{5}\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(\left(-\dfrac{117}{7}\right)\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{2}{7}\right)+\left(-\dfrac{40}{3}\right)\times8\times\left(-\dfrac{55}{7}\right)\times8-\dfrac{40}{3}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-6\right)\times8\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{12426}{77}\right)\times\dfrac{7}{5}\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(\left(-\dfrac{117}{7}\right)\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{2}{7}\right)+\left(-\dfrac{40}{3}\right)\times8\times\left(-\dfrac{55}{7}\right)\times8-\dfrac{40}{3}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-6\right)\times8\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{12426}{77}\right)\times\dfrac{7}{5}\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(\dfrac{3939}{28}\times\left(-\dfrac{2}{7}\right)+\left(-\dfrac{40}{3}\right)\times8\times\left(-\dfrac{55}{7}\right)\times8-\dfrac{40}{3}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-6\right)\times8\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{12426}{77}\right)\times\dfrac{7}{5}\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(-\dfrac{3939}{98}+\left(-\dfrac{40}{3}\right)\times8\times\left(-\dfrac{55}{7}\right)\times8-\dfrac{40}{3}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-6\right)\times8\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{12426}{77}\right)\times\dfrac{7}{5}\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(-\dfrac{3939}{98}+\left(-\dfrac{320}{3}\right)\times\left(-\dfrac{55}{7}\right)\times8-\dfrac{40}{3}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-6\right)\times8\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{12426}{77}\right)\times\dfrac{7}{5}\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(-\dfrac{3939}{98}+\dfrac{17600}{21}\times8-\dfrac{40}{3}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-6\right)\times8\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{12426}{77}\right)\times\dfrac{7}{5}\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(-\dfrac{3939}{98}+\dfrac{140800}{21}-\dfrac{40}{3}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-48\right)\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{12426}{77}\right)\times\dfrac{7}{5}\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(-\dfrac{3939}{98}+\dfrac{140800}{21}-\dfrac{40}{3}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+404\times\left(-\dfrac{101}{12}\right)\times\left(-\dfrac{12426}{77}\right)\times\dfrac{7}{5}\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(-\dfrac{3939}{98}+\dfrac{140800}{21}-\dfrac{40}{3}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-\dfrac{10201}{3}\right)\times\left(-\dfrac{12426}{77}\right)\times\dfrac{7}{5}\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(-\dfrac{3939}{98}+\dfrac{140800}{21}-\dfrac{40}{3}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-\dfrac{10201}{3}\right)\times\left(-\dfrac{12426}{55}\right)\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(-\dfrac{3939}{98}+\dfrac{140800}{21}-\dfrac{40}{3}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-\dfrac{10201}{3}\right)\times\left(-\dfrac{12426}{55}\right)\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(\dfrac{1959383}{294}-\dfrac{40}{3}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-\dfrac{10201}{3}\right)\times\left(-\dfrac{12426}{55}\right)\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\left(\dfrac{651821}{98}+8\right)\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-\dfrac{10201}{3}\right)\times\left(-\dfrac{12426}{55}\right)\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\dfrac{652605}{98}\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\dfrac{42252542}{55}\times\left(-\dfrac{55}{7}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\dfrac{652605}{98}\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}+\left(-\dfrac{2323889810}{385}\right)\times\dfrac{114}{7}-11+4-\dfrac{55}{7}+\dfrac{652605}{98}\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}-\dfrac{264923438340}{2695}-11+4-\dfrac{55}{7}+\dfrac{652605}{98}\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}-\dfrac{264923438340}{2695}-7-\dfrac{55}{7}+\dfrac{652605}{98}\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}-\dfrac{264923438340}{2695}-\dfrac{104}{7}+\dfrac{652605}{98}\times\dfrac{13}{4}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}-\dfrac{264923438340}{2695}-\dfrac{104}{7}+\dfrac{8483865}{392}\times\left(-6\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}-\dfrac{264923438340}{2695}-\dfrac{104}{7}+\left(-\dfrac{25451595}{196}\right)\times\left(-6\right)\\&=&-\dfrac{2}{7}-\dfrac{7}{5}-\dfrac{55}{7}-\dfrac{264923438340}{2695}-\dfrac{104}{7}+\dfrac{76354785}{98}\\&=&-\dfrac{59}{35}-\dfrac{55}{7}-\dfrac{264923438340}{2695}-\dfrac{104}{7}+\dfrac{76354785}{98}\\&=&-\dfrac{59}{35}-\dfrac{1854464216605}{18865}-\dfrac{104}{7}+\dfrac{76354785}{98}\\&=&-\dfrac{59}{35}-\dfrac{12981251478195}{132055}+\dfrac{76354785}{98}\\&=&-\dfrac{59}{35}-\dfrac{1262079613729935}{12941390}\\&=&-\dfrac{44172787244089735}{452948650}\\ \end{eqnarray*}