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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 \[\left(3+\dfrac{72}{5}+6\times\dfrac{\left(-\dfrac{9}{2}\right)\times\dfrac{26}{5}}{\left(-\dfrac{55}{7}\right)\times\left(-4\right)}\times\left(-4\right)\right)-\left(\left(1+\dfrac{\dfrac{1}{-\dfrac{9}{2}}}{\dfrac{26}{5}}\right)+9\right)\times3\times\left(-6\right)\times\dfrac{26}{5}\times\left(-4\right)\times\dfrac{65}{9}\times6\times\dfrac{\dfrac{\dfrac{65}{9}}{-6}}{3}\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{3-\dfrac{72}{5}-\dfrac{72}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\left(\dfrac{26}{3}+\dfrac{65}{9}\right)\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\left(3+\dfrac{72}{5}+6\times\dfrac{\left(-\dfrac{9}{2}\right)\times\dfrac{26}{5}}{\left(-\dfrac{55}{7}\right)\times\left(-4\right)}\times\left(-4\right)\right)-\left(\left(1+\dfrac{\dfrac{1}{-\dfrac{9}{2}}}{\dfrac{26}{5}}\right)+9\right)\times3\times\left(-6\right)\times\dfrac{26}{5}\times\left(-4\right)\times\dfrac{65}{9}\times6\times\dfrac{\dfrac{\dfrac{65}{9}}{-6}}{3}\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{3-\dfrac{72}{5}-\dfrac{72}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\left(\dfrac{26}{3}+\dfrac{65}{9}\right)\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}=-\dfrac{13796286639798465}{27091189125}\) . Voici le détail : \begin{eqnarray*} X &=&\left(3+\dfrac{72}{5}+6\times\dfrac{-\dfrac{117}{5}}{\left(-\dfrac{55}{7}\right)\times\left(-4\right)}\times\left(-4\right)\right)-\left(\left(1+\dfrac{\dfrac{1}{-\dfrac{9}{2}}}{\dfrac{26}{5}}\right)+9\right)\times3\times\left(-6\right)\times\dfrac{26}{5}\times\left(-4\right)\times\dfrac{65}{9}\times6\times\dfrac{\dfrac{\dfrac{65}{9}}{-6}}{3}\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{3-\dfrac{72}{5}-\dfrac{72}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\left(\dfrac{26}{3}+\dfrac{65}{9}\right)\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\dfrac{-\dfrac{117}{5}}{\dfrac{220}{7}}\times\left(-4\right)\right)-\left(\left(1+\dfrac{\dfrac{1}{-\dfrac{9}{2}}}{\dfrac{26}{5}}\right)+9\right)\times3\times\left(-6\right)\times\dfrac{26}{5}\times\left(-4\right)\times\dfrac{65}{9}\times6\times\dfrac{\dfrac{\dfrac{65}{9}}{-6}}{3}\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{3-\dfrac{72}{5}-\dfrac{72}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\left(\dfrac{26}{3}+\dfrac{65}{9}\right)\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\dfrac{-\dfrac{117}{5}}{\dfrac{220}{7}}\times\left(-4\right)\right)-\left(\left(1+\dfrac{-\dfrac{2}{9}}{\dfrac{26}{5}}\right)+9\right)\times3\times\left(-6\right)\times\dfrac{26}{5}\times\left(-4\right)\times\dfrac{65}{9}\times6\times\dfrac{\dfrac{\dfrac{65}{9}}{-6}}{3}\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{3-\dfrac{72}{5}-\dfrac{72}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\left(\dfrac{26}{3}+\dfrac{65}{9}\right)\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\dfrac{-\dfrac{117}{5}}{\dfrac{220}{7}}\times\left(-4\right)\right)-\left(\left(1-\dfrac{5}{117}\right)+9\right)\times3\times\left(-6\right)\times\dfrac{26}{5}\times\left(-4\right)\times\dfrac{65}{9}\times6\times\dfrac{\dfrac{\dfrac{65}{9}}{-6}}{3}\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{3-\dfrac{72}{5}-\dfrac{72}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\left(\dfrac{26}{3}+\dfrac{65}{9}\right)\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\dfrac{-\dfrac{117}{5}}{\dfrac{220}{7}}\times\left(-4\right)\right)-\left(\left(1-\dfrac{5}{117}\right)+9\right)\times3\times\left(-\dfrac{156}{5}\right)\times\left(-4\right)\times\dfrac{65}{9}\times6\times\dfrac{\dfrac{\dfrac{65}{9}}{-6}}{3}\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{3-\dfrac{72}{5}-\dfrac{72}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\left(\dfrac{26}{3}+\dfrac{65}{9}\right)\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\dfrac{-\dfrac{117}{5}}{\dfrac{220}{7}}\times\left(-4\right)\right)-\left(\left(1-\dfrac{5}{117}\right)+9\right)\times3\times\dfrac{624}{5}\times\dfrac{65}{9}\times6\times\dfrac{\dfrac{\dfrac{65}{9}}{-6}}{3}\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{3-\dfrac{72}{5}-\dfrac{72}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\left(\dfrac{26}{3}+\dfrac{65}{9}\right)\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\dfrac{-\dfrac{117}{5}}{\dfrac{220}{7}}\times\left(-4\right)\right)-\left(\left(1-\dfrac{5}{117}\right)+9\right)\times3\times\dfrac{624}{5}\times\dfrac{65}{9}\times6\times\dfrac{-\dfrac{65}{54}}{3}\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{3-\dfrac{72}{5}-\dfrac{72}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\left(\dfrac{26}{3}+\dfrac{65}{9}\right)\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\dfrac{-\dfrac{117}{5}}{\dfrac{220}{7}}\times\left(-4\right)\right)-\left(\left(1-\dfrac{5}{117}\right)+9\right)\times3\times\dfrac{624}{5}\times\dfrac{65}{9}\times6\times\left(-\dfrac{65}{162}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{3-\dfrac{72}{5}-\dfrac{72}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\left(\dfrac{26}{3}+\dfrac{65}{9}\right)\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\dfrac{-\dfrac{117}{5}}{\dfrac{220}{7}}\times\left(-4\right)\right)-\left(\left(1-\dfrac{5}{117}\right)+9\right)\times3\times\dfrac{624}{5}\times\dfrac{65}{9}\times6\times\left(-\dfrac{65}{162}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{57}{5}-\dfrac{72}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\left(\dfrac{26}{3}+\dfrac{65}{9}\right)\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\dfrac{-\dfrac{117}{5}}{\dfrac{220}{7}}\times\left(-4\right)\right)-\left(\left(1-\dfrac{5}{117}\right)+9\right)\times3\times\dfrac{624}{5}\times\dfrac{65}{9}\times6\times\left(-\dfrac{65}{162}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{129}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\left(\dfrac{26}{3}+\dfrac{65}{9}\right)\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\dfrac{-\dfrac{117}{5}}{\dfrac{220}{7}}\times\left(-4\right)\right)-\left(\left(1-\dfrac{5}{117}\right)+9\right)\times3\times\dfrac{624}{5}\times\dfrac{65}{9}\times6\times\left(-\dfrac{65}{162}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{129}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\dfrac{143}{9}\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\left(-\dfrac{819}{1100}\right)\times\left(-4\right)\right)-\left(\left(1-\dfrac{5}{117}\right)+9\right)\times3\times\dfrac{624}{5}\times\dfrac{65}{9}\times6\times\left(-\dfrac{65}{162}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{129}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\dfrac{143}{9}\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\left(-\dfrac{819}{1100}\right)\times\left(-4\right)\right)-\left(\dfrac{112}{117}+9\right)\times3\times\dfrac{624}{5}\times\dfrac{65}{9}\times6\times\left(-\dfrac{65}{162}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{129}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\dfrac{143}{9}\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\left(-\dfrac{819}{1100}\right)\times\left(-4\right)\right)-\left(\dfrac{112}{117}+9\right)\times3\times\dfrac{2704}{3}\times6\times\left(-\dfrac{65}{162}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{129}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\dfrac{143}{9}\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\left(-\dfrac{819}{1100}\right)\times\left(-4\right)\right)-\left(\dfrac{112}{117}+9\right)\times3\times\dfrac{2704}{3}\times\left(-\dfrac{65}{27}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{129}{5}+\dfrac{26}{3}+\dfrac{26}{5}\times\dfrac{143}{9}\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\left(-\dfrac{819}{1100}\right)\times\left(-4\right)\right)-\left(\dfrac{112}{117}+9\right)\times3\times\dfrac{2704}{3}\times\left(-\dfrac{65}{27}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{257}{15}+\dfrac{26}{5}\times\dfrac{143}{9}\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\left(-\dfrac{819}{1100}\right)\times\left(-4\right)\right)-\left(\dfrac{112}{117}+9\right)\times3\times\dfrac{2704}{3}\times\left(-\dfrac{65}{27}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{257}{15}+\dfrac{3718}{45}\times\left(-4\right)}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+6\times\left(-\dfrac{819}{1100}\right)\times\left(-4\right)\right)-\left(\dfrac{112}{117}+9\right)\times3\times\dfrac{2704}{3}\times\left(-\dfrac{65}{27}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{257}{15}-\dfrac{14872}{45}}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+\left(-\dfrac{2457}{550}\right)\times\left(-4\right)\right)-\left(\dfrac{112}{117}+9\right)\times3\times\dfrac{2704}{3}\times\left(-\dfrac{65}{27}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{257}{15}-\dfrac{14872}{45}}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+\dfrac{4914}{275}\right)-\left(\dfrac{112}{117}+9\right)\times3\times\dfrac{2704}{3}\times\left(-\dfrac{65}{27}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{257}{15}-\dfrac{14872}{45}}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+\dfrac{4914}{275}\right)-\dfrac{1165}{117}\times3\times\dfrac{2704}{3}\times\left(-\dfrac{65}{27}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{257}{15}-\dfrac{14872}{45}}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+\dfrac{4914}{275}\right)-\dfrac{1165}{117}\times2704\times\left(-\dfrac{65}{27}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{257}{15}-\dfrac{14872}{45}}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+\dfrac{4914}{275}\right)-\dfrac{1165}{117}\times\left(-\dfrac{175760}{27}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{257}{15}-\dfrac{14872}{45}}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(3+\dfrac{72}{5}+\dfrac{4914}{275}\right)-\dfrac{1165}{117}\times\left(-\dfrac{175760}{27}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{15643}{45}}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\left(\dfrac{87}{5}+\dfrac{4914}{275}\right)-\dfrac{1165}{117}\times\left(-\dfrac{175760}{27}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{15643}{45}}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\dfrac{9699}{275}-\dfrac{1165}{117}\times\left(-\dfrac{175760}{27}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{15643}{45}}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\dfrac{9699}{275}-\left(-\dfrac{15750800}{243}\right)\times\left(-\dfrac{55}{7}\right)-\dfrac{\dfrac{-\dfrac{15643}{45}}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\dfrac{9699}{275}-\dfrac{866294000}{1701}-\dfrac{\dfrac{-\dfrac{15643}{45}}{\dfrac{143}{7}}}{-\dfrac{9}{2}}\\&=&\dfrac{9699}{275}-\dfrac{866294000}{1701}-\dfrac{-\dfrac{109501}{6435}}{-\dfrac{9}{2}}\\&=&\dfrac{9699}{275}-\dfrac{866294000}{1701}-\dfrac{219002}{57915}\\&=&-\dfrac{238214352001}{467775}-\dfrac{219002}{57915}\\&=&-\dfrac{13796286639798465}{27091189125}\\ \end{eqnarray*}