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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 \[\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(\left(-\dfrac{35}{2}\right)\times\dfrac{17}{2}\times\dfrac{46}{5}\times\left(-\dfrac{30}{7}\right)\times2+\left(\dfrac{17}{2}-\dfrac{50}{3}-\dfrac{50}{3}\right)+\dfrac{35}{2}+\dfrac{50}{3}-\left(-\dfrac{43}{4}\right)\times2+\dfrac{\dfrac{\dfrac{-\dfrac{50}{3}}{\dfrac{46}{5}\times\dfrac{46}{5}}}{-\dfrac{43}{4}}}{-9}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(\left(-\dfrac{35}{2}\right)\times\dfrac{17}{2}\times\dfrac{46}{5}\times\left(-\dfrac{30}{7}\right)\times2+\left(\dfrac{17}{2}-\dfrac{50}{3}-\dfrac{50}{3}\right)+\dfrac{35}{2}+\dfrac{50}{3}-\left(-\dfrac{43}{4}\right)\times2+\dfrac{\dfrac{\dfrac{-\dfrac{50}{3}}{\dfrac{46}{5}\times\dfrac{46}{5}}}{-\dfrac{43}{4}}}{-9}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)=-\dfrac{364720512636000}{1057753788588}\) . Voici le détail : \begin{eqnarray*} X &=&\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(\left(-\dfrac{595}{4}\right)\times\dfrac{46}{5}\times\left(-\dfrac{30}{7}\right)\times2+\left(\dfrac{17}{2}-\dfrac{50}{3}-\dfrac{50}{3}\right)+\dfrac{35}{2}+\dfrac{50}{3}-\left(-\dfrac{43}{4}\right)\times2+\dfrac{\dfrac{\dfrac{-\dfrac{50}{3}}{\dfrac{46}{5}\times\dfrac{46}{5}}}{-\dfrac{43}{4}}}{-9}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(\left(-\dfrac{2737}{2}\right)\times\left(-\dfrac{30}{7}\right)\times2+\left(\dfrac{17}{2}-\dfrac{50}{3}-\dfrac{50}{3}\right)+\dfrac{35}{2}+\dfrac{50}{3}-\left(-\dfrac{43}{4}\right)\times2+\dfrac{\dfrac{\dfrac{-\dfrac{50}{3}}{\dfrac{46}{5}\times\dfrac{46}{5}}}{-\dfrac{43}{4}}}{-9}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(5865\times2+\left(\dfrac{17}{2}-\dfrac{50}{3}-\dfrac{50}{3}\right)+\dfrac{35}{2}+\dfrac{50}{3}-\left(-\dfrac{43}{4}\right)\times2+\dfrac{\dfrac{\dfrac{-\dfrac{50}{3}}{\dfrac{46}{5}\times\dfrac{46}{5}}}{-\dfrac{43}{4}}}{-9}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(5865\times2+\left(-\dfrac{49}{6}-\dfrac{50}{3}\right)+\dfrac{35}{2}+\dfrac{50}{3}-\left(-\dfrac{43}{4}\right)\times2+\dfrac{\dfrac{\dfrac{-\dfrac{50}{3}}{\dfrac{46}{5}\times\dfrac{46}{5}}}{-\dfrac{43}{4}}}{-9}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(5865\times2-\dfrac{149}{6}+\dfrac{35}{2}+\dfrac{50}{3}-\left(-\dfrac{43}{4}\right)\times2+\dfrac{\dfrac{\dfrac{-\dfrac{50}{3}}{\dfrac{46}{5}\times\dfrac{46}{5}}}{-\dfrac{43}{4}}}{-9}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(5865\times2-\dfrac{149}{6}+\dfrac{35}{2}+\dfrac{50}{3}+\dfrac{43}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{50}{3}}{\dfrac{46}{5}\times\dfrac{46}{5}}}{-\dfrac{43}{4}}}{-9}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(5865\times2-\dfrac{149}{6}+\dfrac{35}{2}+\dfrac{50}{3}+\dfrac{43}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{50}{3}}{\dfrac{2116}{25}}}{-\dfrac{43}{4}}}{-9}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(11730-\dfrac{149}{6}+\dfrac{35}{2}+\dfrac{50}{3}+\dfrac{43}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{50}{3}}{\dfrac{2116}{25}}}{-\dfrac{43}{4}}}{-9}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(11730-\dfrac{22}{3}+\dfrac{50}{3}+\dfrac{43}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{50}{3}}{\dfrac{2116}{25}}}{-\dfrac{43}{4}}}{-9}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(11730+\dfrac{28}{3}+\dfrac{43}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{50}{3}}{\dfrac{2116}{25}}}{-\dfrac{43}{4}}}{-9}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(11730+\dfrac{185}{6}+\dfrac{\dfrac{\dfrac{-\dfrac{50}{3}}{\dfrac{2116}{25}}}{-\dfrac{43}{4}}}{-9}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(11730+\dfrac{185}{6}+\dfrac{\dfrac{-\dfrac{625}{3174}}{-\dfrac{43}{4}}}{-9}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(11730+\dfrac{185}{6}+\dfrac{\dfrac{1250}{68241}}{-9}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{30}{7}}{\dfrac{101}{7}}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(11730+\dfrac{185}{6}-\dfrac{1250}{614169}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{\dfrac{-\dfrac{30}{101}}{\dfrac{29}{3}}}{-\dfrac{35}{2}}\times\left(\left(11730+\dfrac{185}{6}-\dfrac{1250}{614169}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{-\dfrac{90}{2929}}{-\dfrac{35}{2}}\times\left(\left(11730+\dfrac{185}{6}-\dfrac{1250}{614169}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{36}{20503}\times\left(\left(11730+\dfrac{185}{6}-\dfrac{1250}{614169}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{36}{20503}\times\left(\left(\dfrac{70565}{6}-\dfrac{1250}{614169}\right)+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{50}{3}\right)\times\dfrac{36}{20503}\times\left(\dfrac{43338827985}{3685014}+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{600}{20503}\right)\times\left(\dfrac{43338827985}{3685014}+\dfrac{30}{7}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{600}{20503}\right)\times\left(\dfrac{303482346315}{25795098}+\dfrac{35}{2}\right)\\&=&\left(-\dfrac{600}{20503}\right)\times\dfrac{607867521060}{51590196}\\&=&-\dfrac{364720512636000}{1057753788588}\\ \end{eqnarray*}