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Exercice
Calculer \[3\times3\times\left(-\dfrac{60}{7}+12-\dfrac{60}{7}\right)\times\dfrac{\dfrac{10}{3\times\left(-6\right)}}{10}-\left(-3+\dfrac{-9-\dfrac{40}{3}+\dfrac{-3}{12}}{\dfrac{13}{2}}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{\dfrac{\dfrac{\dfrac{-3}{-\dfrac{121}{4}}}{-6}}{\dfrac{118}{5}}}-3-\dfrac{121}{4}\right)\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=3\times3\times\left(-\dfrac{60}{7}+12-\dfrac{60}{7}\right)\times\dfrac{\dfrac{10}{3\times\left(-6\right)}}{10}-\left(-3+\dfrac{-9-\dfrac{40}{3}+\dfrac{-3}{12}}{\dfrac{13}{2}}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{\dfrac{\dfrac{\dfrac{-3}{-\dfrac{121}{4}}}{-6}}{\dfrac{118}{5}}}-3-\dfrac{121}{4}\right)=-\dfrac{6970637}{5460}\) . Voici le détail :
\begin{eqnarray*}
X &=&3\times3\times\left(-\dfrac{60}{7}+\dfrac{24}{7}\right)\times\dfrac{\dfrac{10}{3\times\left(-6\right)}}{10}-\left(-3+\dfrac{-9-\dfrac{40}{3}+\dfrac{-3}{12}}{\dfrac{13}{2}}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{\dfrac{\dfrac{\dfrac{-3}{-\dfrac{121}{4}}}{-6}}{\dfrac{118}{5}}}-3-\dfrac{121}{4}\right)\\&=&3\times3\times\left(-\dfrac{60}{7}+\dfrac{24}{7}\right)\times\dfrac{\dfrac{10}{-18}}{10}-\left(-3+\dfrac{-9-\dfrac{40}{3}+\dfrac{-3}{12}}{\dfrac{13}{2}}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{\dfrac{\dfrac{\dfrac{-3}{-\dfrac{121}{4}}}{-6}}{\dfrac{118}{5}}}-3-\dfrac{121}{4}\right)\\&=&3\times3\times\left(-\dfrac{60}{7}+\dfrac{24}{7}\right)\times\dfrac{\dfrac{10}{-18}}{10}-\left(-3+\dfrac{-9-\dfrac{40}{3}-\dfrac{1}{4}}{\dfrac{13}{2}}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{\dfrac{\dfrac{\dfrac{-3}{-\dfrac{121}{4}}}{-6}}{\dfrac{118}{5}}}-3-\dfrac{121}{4}\right)\\&=&3\times3\times\left(-\dfrac{60}{7}+\dfrac{24}{7}\right)\times\dfrac{\dfrac{10}{-18}}{10}-\left(-3+\dfrac{-9-\dfrac{40}{3}-\dfrac{1}{4}}{\dfrac{13}{2}}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{\dfrac{\dfrac{\dfrac{12}{121}}{-6}}{\dfrac{118}{5}}}-3-\dfrac{121}{4}\right)\\&=&3\times3\times\left(-\dfrac{60}{7}+\dfrac{24}{7}\right)\times\dfrac{\dfrac{10}{-18}}{10}-\left(-3+\dfrac{-9-\dfrac{40}{3}-\dfrac{1}{4}}{\dfrac{13}{2}}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{\dfrac{-\dfrac{2}{121}}{\dfrac{118}{5}}}-3-\dfrac{121}{4}\right)\\&=&3\times3\times\left(-\dfrac{36}{7}\right)\times\dfrac{\dfrac{10}{-18}}{10}-\left(-3+\dfrac{-9-\dfrac{40}{3}-\dfrac{1}{4}}{\dfrac{13}{2}}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{\dfrac{-\dfrac{2}{121}}{\dfrac{118}{5}}}-3-\dfrac{121}{4}\right)\\&=&3\times3\times\left(-\dfrac{36}{7}\right)\times\dfrac{-\dfrac{5}{9}}{10}-\left(-3+\dfrac{-9-\dfrac{40}{3}-\dfrac{1}{4}}{\dfrac{13}{2}}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{\dfrac{-\dfrac{2}{121}}{\dfrac{118}{5}}}-3-\dfrac{121}{4}\right)\\&=&3\times3\times\left(-\dfrac{36}{7}\right)\times\left(-\dfrac{1}{18}\right)-\left(-3+\dfrac{-9-\dfrac{40}{3}-\dfrac{1}{4}}{\dfrac{13}{2}}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{\dfrac{-\dfrac{2}{121}}{\dfrac{118}{5}}}-3-\dfrac{121}{4}\right)\\&=&3\times3\times\left(-\dfrac{36}{7}\right)\times\left(-\dfrac{1}{18}\right)-\left(-3+\dfrac{-\dfrac{67}{3}-\dfrac{1}{4}}{\dfrac{13}{2}}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{\dfrac{-\dfrac{2}{121}}{\dfrac{118}{5}}}-3-\dfrac{121}{4}\right)\\&=&3\times3\times\left(-\dfrac{36}{7}\right)\times\left(-\dfrac{1}{18}\right)-\left(-3+\dfrac{-\dfrac{271}{12}}{\dfrac{13}{2}}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{\dfrac{-\dfrac{2}{121}}{\dfrac{118}{5}}}-3-\dfrac{121}{4}\right)\\&=&3\times3\times\left(-\dfrac{36}{7}\right)\times\left(-\dfrac{1}{18}\right)-\left(-3+\dfrac{-\dfrac{271}{12}}{\dfrac{13}{2}}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{-\dfrac{5}{7139}}-3-\dfrac{121}{4}\right)\\&=&3\times\left(-\dfrac{108}{7}\right)\times\left(-\dfrac{1}{18}\right)-\left(-3+\dfrac{-\dfrac{271}{12}}{\dfrac{13}{2}}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{-\dfrac{5}{7139}}-3-\dfrac{121}{4}\right)\\&=&3\times\dfrac{6}{7}-\left(-3+\dfrac{-\dfrac{271}{12}}{\dfrac{13}{2}}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{-\dfrac{5}{7139}}-3-\dfrac{121}{4}\right)\\&=&3\times\dfrac{6}{7}-\left(-3-\dfrac{271}{78}\right)-\left(1+\dfrac{\dfrac{-6}{\dfrac{13}{2}}}{-\dfrac{5}{7139}}-3-\dfrac{121}{4}\right)\\&=&3\times\dfrac{6}{7}-\left(-3-\dfrac{271}{78}\right)-\left(1+\dfrac{-\dfrac{12}{13}}{-\dfrac{5}{7139}}-3-\dfrac{121}{4}\right)\\&=&3\times\dfrac{6}{7}-\left(-3-\dfrac{271}{78}\right)-\left(1+\dfrac{85668}{65}-3-\dfrac{121}{4}\right)\\&=&3\times\dfrac{6}{7}-\left(-3-\dfrac{271}{78}\right)-\left(1+\dfrac{85668}{65}-\dfrac{133}{4}\right)\\&=&\dfrac{18}{7}-\left(-3-\dfrac{271}{78}\right)-\left(1+\dfrac{85668}{65}-\dfrac{133}{4}\right)\\&=&\dfrac{18}{7}+\dfrac{505}{78}-\left(1+\dfrac{85668}{65}-\dfrac{133}{4}\right)\\&=&\dfrac{18}{7}+\dfrac{505}{78}-\left(\dfrac{85733}{65}-\dfrac{133}{4}\right)\\&=&\dfrac{18}{7}+\dfrac{505}{78}-\dfrac{334287}{260}\\&=&\dfrac{4939}{546}-\dfrac{334287}{260}\\&=&-\dfrac{6970637}{5460}\\
\end{eqnarray*}