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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 \[\dfrac{74}{7}\times\left(\left(\left(-\dfrac{45}{2}\right)\times\dfrac{22}{3}\times\dfrac{71}{6}\times11-\left(\dfrac{71}{6}+\dfrac{22}{3}+11+2\right)-\left(-\dfrac{45}{2}+\dfrac{71}{6}+10\right)\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2-\dfrac{-11}{\dfrac{85}{9}}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{\left(-\dfrac{45}{2}\right)\times10\times\left(-10\right)}{\dfrac{141}{8}}}{\dfrac{71}{6}+10-\dfrac{95}{3}-11}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{74}{7}\times\left(\left(\left(-\dfrac{45}{2}\right)\times\dfrac{22}{3}\times\dfrac{71}{6}\times11-\left(\dfrac{71}{6}+\dfrac{22}{3}+11+2\right)-\left(-\dfrac{45}{2}+\dfrac{71}{6}+10\right)\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2-\dfrac{-11}{\dfrac{85}{9}}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{\left(-\dfrac{45}{2}\right)\times10\times\left(-10\right)}{\dfrac{141}{8}}}{\dfrac{71}{6}+10-\dfrac{95}{3}-11}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}=\dfrac{91056186745531500}{45409896}\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{74}{7}\times\left(\left(\left(-\dfrac{45}{2}\right)\times\dfrac{22}{3}\times\dfrac{71}{6}\times11-\left(\dfrac{71}{6}+\dfrac{22}{3}+11+2\right)-\left(-\dfrac{45}{2}+\dfrac{71}{6}+10\right)\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2+\dfrac{99}{85}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{\left(-\dfrac{45}{2}\right)\times10\times\left(-10\right)}{\dfrac{141}{8}}}{\dfrac{71}{6}+10-\dfrac{95}{3}-11}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(\left(-\dfrac{45}{2}\right)\times\dfrac{22}{3}\times\dfrac{71}{6}\times11-\left(\dfrac{71}{6}+\dfrac{22}{3}+11+2\right)-\left(-\dfrac{45}{2}+\dfrac{71}{6}+10\right)\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2+\dfrac{99}{85}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{\left(-225\right)\times\left(-10\right)}{\dfrac{141}{8}}}{\dfrac{71}{6}+10-\dfrac{95}{3}-11}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(\left(-\dfrac{45}{2}\right)\times\dfrac{22}{3}\times\dfrac{71}{6}\times11-\left(\dfrac{71}{6}+\dfrac{22}{3}+11+2\right)-\left(-\dfrac{45}{2}+\dfrac{71}{6}+10\right)\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2+\dfrac{99}{85}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{2250}{\dfrac{141}{8}}}{\dfrac{71}{6}+10-\dfrac{95}{3}-11}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(\left(-\dfrac{45}{2}\right)\times\dfrac{22}{3}\times\dfrac{71}{6}\times11-\left(\dfrac{71}{6}+\dfrac{22}{3}+11+2\right)-\left(-\dfrac{45}{2}+\dfrac{71}{6}+10\right)\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2+\dfrac{99}{85}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{2250}{\dfrac{141}{8}}}{\dfrac{131}{6}-\dfrac{95}{3}-11}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(\left(-\dfrac{45}{2}\right)\times\dfrac{22}{3}\times\dfrac{71}{6}\times11-\left(\dfrac{71}{6}+\dfrac{22}{3}+11+2\right)-\left(-\dfrac{45}{2}+\dfrac{71}{6}+10\right)\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2+\dfrac{99}{85}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{2250}{\dfrac{141}{8}}}{-\dfrac{59}{6}-11}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(\left(-\dfrac{45}{2}\right)\times\dfrac{22}{3}\times\dfrac{71}{6}\times11-\left(\dfrac{71}{6}+\dfrac{22}{3}+11+2\right)-\left(-\dfrac{45}{2}+\dfrac{71}{6}+10\right)\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2+\dfrac{99}{85}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{2250}{\dfrac{141}{8}}}{-\dfrac{125}{6}}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(\left(-165\right)\times\dfrac{71}{6}\times11-\left(\dfrac{71}{6}+\dfrac{22}{3}+11+2\right)-\left(-\dfrac{45}{2}+\dfrac{71}{6}+10\right)\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2+\dfrac{99}{85}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{2250}{\dfrac{141}{8}}}{-\dfrac{125}{6}}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(\left(-\dfrac{3905}{2}\right)\times11-\left(\dfrac{71}{6}+\dfrac{22}{3}+11+2\right)-\left(-\dfrac{45}{2}+\dfrac{71}{6}+10\right)\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2+\dfrac{99}{85}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{2250}{\dfrac{141}{8}}}{-\dfrac{125}{6}}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(-\dfrac{42955}{2}-\left(\dfrac{71}{6}+\dfrac{22}{3}+11+2\right)-\left(-\dfrac{45}{2}+\dfrac{71}{6}+10\right)\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2+\dfrac{99}{85}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{2250}{\dfrac{141}{8}}}{-\dfrac{125}{6}}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(-\dfrac{42955}{2}-\left(\dfrac{115}{6}+11+2\right)-\left(-\dfrac{45}{2}+\dfrac{71}{6}+10\right)\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2+\dfrac{99}{85}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{2250}{\dfrac{141}{8}}}{-\dfrac{125}{6}}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(-\dfrac{42955}{2}-\left(\dfrac{181}{6}+2\right)-\left(-\dfrac{45}{2}+\dfrac{71}{6}+10\right)\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2+\dfrac{99}{85}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{2250}{\dfrac{141}{8}}}{-\dfrac{125}{6}}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(-\dfrac{42955}{2}-\dfrac{193}{6}-\left(-\dfrac{45}{2}+\dfrac{71}{6}+10\right)\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2+\dfrac{99}{85}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{2250}{\dfrac{141}{8}}}{-\dfrac{125}{6}}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(-\dfrac{42955}{2}-\dfrac{193}{6}-\left(-\dfrac{32}{3}+10\right)\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2+\dfrac{99}{85}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{2250}{\dfrac{141}{8}}}{-\dfrac{125}{6}}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(-\dfrac{42955}{2}-\dfrac{193}{6}+\dfrac{2}{3}\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\left(2+\dfrac{99}{85}\right)\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{2250}{\dfrac{141}{8}}}{-\dfrac{125}{6}}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(-\dfrac{42955}{2}-\dfrac{193}{6}+\dfrac{2}{3}\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\dfrac{269}{85}\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{2250}{\dfrac{141}{8}}}{-\dfrac{125}{6}}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(-\dfrac{42955}{2}-\dfrac{193}{6}+\dfrac{2}{3}\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\dfrac{269}{85}\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{\dfrac{\dfrac{6000}{47}}{-\dfrac{125}{6}}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(-\dfrac{42955}{2}-\dfrac{193}{6}+\dfrac{2}{3}\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\dfrac{269}{85}\times\dfrac{85}{9}\times\left(-11\right)+2+\dfrac{-\dfrac{288}{47}}{2}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(-\dfrac{42955}{2}-\dfrac{193}{6}+\dfrac{2}{3}\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\dfrac{269}{85}\times\dfrac{85}{9}\times\left(-11\right)+2-\dfrac{144}{47}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(\left(-\dfrac{64529}{3}+\dfrac{2}{3}\right)-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\dfrac{269}{85}\times\dfrac{85}{9}\times\left(-11\right)+2-\dfrac{144}{47}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(-21509-\dfrac{85}{9}-\left(\dfrac{85}{9}+8-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\dfrac{269}{85}\times\dfrac{85}{9}\times\left(-11\right)+2-\dfrac{144}{47}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(-21509-\dfrac{85}{9}-\left(\dfrac{157}{9}-\dfrac{141}{8}\right)+8\right)\times\left(10+\dfrac{95}{3}\times\dfrac{269}{85}\times\dfrac{85}{9}\times\left(-11\right)+2-\dfrac{144}{47}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(-21509-\dfrac{85}{9}+\dfrac{13}{72}+8\right)\times\left(10+\dfrac{95}{3}\times\dfrac{269}{85}\times\dfrac{85}{9}\times\left(-11\right)+2-\dfrac{144}{47}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(-21509-\dfrac{85}{9}+\dfrac{13}{72}+8\right)\times\left(10+\dfrac{5111}{51}\times\dfrac{85}{9}\times\left(-11\right)+2-\dfrac{144}{47}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(-21509-\dfrac{85}{9}+\dfrac{13}{72}+8\right)\times\left(10+\dfrac{25555}{27}\times\left(-11\right)+2-\dfrac{144}{47}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(-21509-\dfrac{85}{9}+\dfrac{13}{72}+8\right)\times\left(10-\dfrac{281105}{27}+2-\dfrac{144}{47}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(-21509-\dfrac{85}{9}+\dfrac{13}{72}+8\right)\times\left(10-\dfrac{281105}{27}-\dfrac{50}{47}-\dfrac{45}{2}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(-21509-\dfrac{85}{9}+\dfrac{13}{72}+8\right)\times\left(10-\dfrac{281105}{27}-\dfrac{2215}{94}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(-\dfrac{193666}{9}+\dfrac{13}{72}+8\right)\times\left(10-\dfrac{281105}{27}-\dfrac{2215}{94}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times\left(-\dfrac{1549315}{72}+8\right)\times\left(10-\dfrac{281105}{27}-\dfrac{2215}{94}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times-\dfrac{1548739}{72}\times\left(10-\dfrac{281105}{27}-\dfrac{2215}{94}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times-\dfrac{1548739}{72}\times\left(-\dfrac{280835}{27}-\dfrac{2215}{94}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times-\dfrac{1548739}{72}\times\left(-\dfrac{26458295}{2538}-10\right)\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times-\dfrac{1548739}{72}\times-\dfrac{26483675}{2538}\times\dfrac{10}{\dfrac{71}{6}}\\&=&\dfrac{74}{7}\times-\dfrac{1548739}{72}\times-\dfrac{26483675}{2538}\times\dfrac{60}{71}\\&=&\left(-\dfrac{57303343}{252}\right)\times-\dfrac{26483675}{2538}\times\dfrac{60}{71}\\&=&\left(\dfrac{1517603112425525}{639576}\right)\times\dfrac{60}{71}\\&=&\dfrac{91056186745531500}{45409896}\\ \end{eqnarray*}