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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 \[\left(-\dfrac{103}{6}\right)\times\left(3-\dfrac{19}{5}+\dfrac{69}{5}\right)\times\left(-7\right)\times3\times\left(\dfrac{\dfrac{\dfrac{2}{-\dfrac{103}{6}}}{-\dfrac{103}{6}}}{-\dfrac{21}{5}}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\left(-\dfrac{103}{6}\right)\times\left(-7\right)\times\left(-\dfrac{133}{10}\right)\times\left(-\dfrac{19}{5}\right)}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{\dfrac{127}{5}}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{27}{4}}}{\dfrac{19}{6}}}{-9}\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\left(-\dfrac{103}{6}\right)\times\left(3-\dfrac{19}{5}+\dfrac{69}{5}\right)\times\left(-7\right)\times3\times\left(\dfrac{\dfrac{\dfrac{2}{-\dfrac{103}{6}}}{-\dfrac{103}{6}}}{-\dfrac{21}{5}}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\left(-\dfrac{103}{6}\right)\times\left(-7\right)\times\left(-\dfrac{133}{10}\right)\times\left(-\dfrac{19}{5}\right)}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{\dfrac{127}{5}}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{27}{4}}}{\dfrac{19}{6}}}{-9}=-\dfrac{9.4594453411977E+20}{4746449421907200}\) . Voici le détail : \begin{eqnarray*} X &=&\left(-\dfrac{103}{6}\right)\times\left(-\dfrac{4}{5}+\dfrac{69}{5}\right)\times\left(-7\right)\times3\times\left(\dfrac{\dfrac{\dfrac{2}{-\dfrac{103}{6}}}{-\dfrac{103}{6}}}{-\dfrac{21}{5}}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\left(-\dfrac{103}{6}\right)\times\left(-7\right)\times\left(-\dfrac{133}{10}\right)\times\left(-\dfrac{19}{5}\right)}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{\dfrac{127}{5}}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{27}{4}}}{\dfrac{19}{6}}}{-9}\\&=&\left(-\dfrac{103}{6}\right)\times13\times\left(-7\right)\times3\times\left(\dfrac{\dfrac{\dfrac{2}{-\dfrac{103}{6}}}{-\dfrac{103}{6}}}{-\dfrac{21}{5}}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\left(-\dfrac{103}{6}\right)\times\left(-7\right)\times\left(-\dfrac{133}{10}\right)\times\left(-\dfrac{19}{5}\right)}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{\dfrac{127}{5}}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{27}{4}}}{\dfrac{19}{6}}}{-9}\\&=&\left(-\dfrac{103}{6}\right)\times13\times\left(-7\right)\times3\times\left(\dfrac{\dfrac{-\dfrac{12}{103}}{-\dfrac{103}{6}}}{-\dfrac{21}{5}}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\left(-\dfrac{103}{6}\right)\times\left(-7\right)\times\left(-\dfrac{133}{10}\right)\times\left(-\dfrac{19}{5}\right)}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{\dfrac{127}{5}}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{27}{4}}}{\dfrac{19}{6}}}{-9}\\&=&\left(-\dfrac{103}{6}\right)\times13\times\left(-7\right)\times3\times\left(\dfrac{\dfrac{72}{10609}}{-\dfrac{21}{5}}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\left(-\dfrac{103}{6}\right)\times\left(-7\right)\times\left(-\dfrac{133}{10}\right)\times\left(-\dfrac{19}{5}\right)}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{\dfrac{127}{5}}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{27}{4}}}{\dfrac{19}{6}}}{-9}\\&=&\left(-\dfrac{103}{6}\right)\times13\times\left(-7\right)\times3\times\left(-\dfrac{120}{74263}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\left(-\dfrac{103}{6}\right)\times\left(-7\right)\times\left(-\dfrac{133}{10}\right)\times\left(-\dfrac{19}{5}\right)}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{\dfrac{127}{5}}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{27}{4}}}{\dfrac{19}{6}}}{-9}\\&=&\left(-\dfrac{103}{6}\right)\times13\times\left(-7\right)\times3\times\left(-\dfrac{120}{74263}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{721}{6}\times\left(-\dfrac{133}{10}\right)\times\left(-\dfrac{19}{5}\right)}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{\dfrac{127}{5}}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{27}{4}}}{\dfrac{19}{6}}}{-9}\\&=&\left(-\dfrac{103}{6}\right)\times13\times\left(-7\right)\times3\times\left(-\dfrac{120}{74263}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\left(-\dfrac{95893}{60}\right)\times\left(-\dfrac{19}{5}\right)}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{\dfrac{127}{5}}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{27}{4}}}{\dfrac{19}{6}}}{-9}\\&=&\left(-\dfrac{103}{6}\right)\times13\times\left(-7\right)\times3\times\left(-\dfrac{120}{74263}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{1821967}{300}}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{\dfrac{127}{5}}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{27}{4}}}{\dfrac{19}{6}}}{-9}\\&=&\left(-\dfrac{103}{6}\right)\times13\times\left(-7\right)\times3\times\left(-\dfrac{120}{74263}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{1821967}{300}}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{127}{10}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{27}{4}}}{\dfrac{19}{6}}}{-9}\\&=&\left(-\dfrac{103}{6}\right)\times13\times\left(-7\right)\times3\times\left(-\dfrac{120}{74263}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{1821967}{300}}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{127}{10}+\dfrac{\dfrac{-\dfrac{266}{135}}{\dfrac{19}{6}}}{-9}\\&=&\left(-\dfrac{103}{6}\right)\times13\times\left(-7\right)\times3\times\left(-\dfrac{120}{74263}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{1821967}{300}}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{127}{10}+\dfrac{-\dfrac{28}{45}}{-9}\\&=&\left(-\dfrac{103}{6}\right)\times13\times\left(-7\right)\times3\times\left(-\dfrac{120}{74263}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{1821967}{300}}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{127}{10}+\dfrac{28}{405}\\&=&\left(-\dfrac{103}{6}\right)\times\left(-91\right)\times3\times\left(-\dfrac{120}{74263}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{1821967}{300}}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{127}{10}+\dfrac{28}{405}\\&=&\left(-\dfrac{103}{6}\right)\times\left(-273\right)\times\left(-\dfrac{120}{74263}-\dfrac{133}{10}\right)\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{1821967}{300}}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{127}{10}+\dfrac{28}{405}\\&=&\left(-\dfrac{103}{6}\right)\times\left(-273\right)\times-\dfrac{9878179}{742630}\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{\dfrac{-\dfrac{133}{10}}{\dfrac{1821967}{300}}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{127}{10}+\dfrac{28}{405}\\&=&\left(-\dfrac{103}{6}\right)\times\left(-273\right)\times-\dfrac{9878179}{742630}\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{\dfrac{-\dfrac{30}{13699}}{2}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{127}{10}+\dfrac{28}{405}\\&=&\left(-\dfrac{103}{6}\right)\times\left(-273\right)\times-\dfrac{9878179}{742630}\times\dfrac{19}{6}+\dfrac{69}{5}+\dfrac{-\dfrac{15}{13699}}{3}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{127}{10}+\dfrac{28}{405}\\&=&\left(-\dfrac{103}{6}\right)\times\left(-273\right)\times-\dfrac{9878179}{742630}\times\dfrac{19}{6}+\dfrac{69}{5}-\dfrac{5}{13699}+\left(-\dfrac{81}{2}\right)\times\dfrac{19}{6}\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{127}{10}+\dfrac{28}{405}\\&=&\left(-\dfrac{103}{6}\right)\times\left(-273\right)\times-\dfrac{9878179}{742630}\times\dfrac{19}{6}+\dfrac{69}{5}-\dfrac{5}{13699}+\left(-\dfrac{513}{4}\right)\times\dfrac{119}{8}+3-\dfrac{133}{10}+\dfrac{127}{10}+\dfrac{28}{405}\\&=&\left(-\dfrac{103}{6}\right)\times\left(-273\right)\times-\dfrac{9878179}{742630}\times\dfrac{19}{6}+\dfrac{69}{5}-\dfrac{5}{13699}-\dfrac{61047}{32}+3-\dfrac{133}{10}+\dfrac{127}{10}+\dfrac{28}{405}\\&=&\left(-\dfrac{103}{6}\right)\times\left(-273\right)\times-\dfrac{9878179}{742630}\times\dfrac{19}{6}+\dfrac{69}{5}-\dfrac{5}{13699}-\dfrac{61047}{32}-\dfrac{103}{10}+\dfrac{127}{10}+\dfrac{28}{405}\\&=&\left(-\dfrac{103}{6}\right)\times\left(-273\right)\times-\dfrac{9878179}{742630}\times\dfrac{19}{6}+\dfrac{69}{5}-\dfrac{5}{13699}-\dfrac{61047}{32}+\dfrac{12}{5}+\dfrac{28}{405}\\&=&\left(-\dfrac{103}{6}\right)\times\left(-273\right)\times-\dfrac{9878179}{742630}\times\dfrac{19}{6}+\dfrac{69}{5}-\dfrac{5}{13699}-\dfrac{61047}{32}+\dfrac{200}{81}\\&=&\left(-\dfrac{103}{6}\right)\times\left(\dfrac{2696742867}{742630}\right)\times\dfrac{19}{6}+\dfrac{69}{5}-\dfrac{5}{13699}-\dfrac{61047}{32}+\dfrac{200}{81}\\&=&\left(-\dfrac{103}{6}\right)\times\left(\dfrac{2696742867}{742630}\right)\times\dfrac{19}{6}+\dfrac{69}{5}-\dfrac{836283013}{438368}+\dfrac{200}{81}\\&=&\left(-\dfrac{103}{6}\right)\times\left(\dfrac{2696742867}{742630}\right)\times\dfrac{19}{6}+\dfrac{69}{5}-\dfrac{67651250453}{35507808}\\&=&-\dfrac{277764515301}{4455780}\times\dfrac{19}{6}+\dfrac{69}{5}-\dfrac{67651250453}{35507808}\\&=&-\dfrac{5277525790719}{26734680}+\dfrac{69}{5}-\dfrac{67651250453}{35507808}\\&=&-\dfrac{5277525790719}{26734680}-\dfrac{335806213513}{177539040}\\&=&-\dfrac{9.4594453411977E+20}{4746449421907200}\\ \end{eqnarray*}