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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 \[\left(-11\right)\times\dfrac{122}{3}\times\left(\left(9+\dfrac{\dfrac{11}{\dfrac{122}{3}}}{12}\right)-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11-\left(-11+\dfrac{108}{11}-9+\dfrac{9}{2}\right)\times\left(6+\dfrac{19}{2}+\dfrac{19}{2}+\dfrac{101}{5}\right)\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(\dfrac{31}{4}-11+\dfrac{19}{2}-\dfrac{83}{2}\right)\times\dfrac{31}{4}\times\dfrac{122}{3}\times\left(9\times\left(9+\dfrac{63}{10}\right)-7-7\right)\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\left(-11\right)\times\dfrac{122}{3}\times\left(\left(9+\dfrac{\dfrac{11}{\dfrac{122}{3}}}{12}\right)-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11-\left(-11+\dfrac{108}{11}-9+\dfrac{9}{2}\right)\times\left(6+\dfrac{19}{2}+\dfrac{19}{2}+\dfrac{101}{5}\right)\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(\dfrac{31}{4}-11+\dfrac{19}{2}-\dfrac{83}{2}\right)\times\dfrac{31}{4}\times\dfrac{122}{3}\times\left(9\times\left(9+\dfrac{63}{10}\right)-7-7\right)=-\dfrac{6.3168221659066E+24}{7085760}\) . Voici le détail : \begin{eqnarray*} X &=&\left(-11\right)\times\dfrac{122}{3}\times\left(\left(9+\dfrac{\dfrac{33}{122}}{12}\right)-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11-\left(-11+\dfrac{108}{11}-9+\dfrac{9}{2}\right)\times\left(6+\dfrac{19}{2}+\dfrac{19}{2}+\dfrac{101}{5}\right)\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(\dfrac{31}{4}-11+\dfrac{19}{2}-\dfrac{83}{2}\right)\times\dfrac{31}{4}\times\dfrac{122}{3}\times\left(9\times\left(9+\dfrac{63}{10}\right)-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\left(9+\dfrac{11}{488}\right)-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11-\left(-11+\dfrac{108}{11}-9+\dfrac{9}{2}\right)\times\left(6+\dfrac{19}{2}+\dfrac{19}{2}+\dfrac{101}{5}\right)\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(\dfrac{31}{4}-11+\dfrac{19}{2}-\dfrac{83}{2}\right)\times\dfrac{31}{4}\times\dfrac{122}{3}\times\left(9\times\left(9+\dfrac{63}{10}\right)-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\left(9+\dfrac{11}{488}\right)-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11-\left(-\dfrac{13}{11}-9+\dfrac{9}{2}\right)\times\left(6+\dfrac{19}{2}+\dfrac{19}{2}+\dfrac{101}{5}\right)\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(\dfrac{31}{4}-11+\dfrac{19}{2}-\dfrac{83}{2}\right)\times\dfrac{31}{4}\times\dfrac{122}{3}\times\left(9\times\left(9+\dfrac{63}{10}\right)-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\left(9+\dfrac{11}{488}\right)-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11-\left(-\dfrac{112}{11}+\dfrac{9}{2}\right)\times\left(6+\dfrac{19}{2}+\dfrac{19}{2}+\dfrac{101}{5}\right)\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(\dfrac{31}{4}-11+\dfrac{19}{2}-\dfrac{83}{2}\right)\times\dfrac{31}{4}\times\dfrac{122}{3}\times\left(9\times\left(9+\dfrac{63}{10}\right)-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\left(9+\dfrac{11}{488}\right)-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{125}{22}\times\left(6+\dfrac{19}{2}+\dfrac{19}{2}+\dfrac{101}{5}\right)\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(\dfrac{31}{4}-11+\dfrac{19}{2}-\dfrac{83}{2}\right)\times\dfrac{31}{4}\times\dfrac{122}{3}\times\left(9\times\left(9+\dfrac{63}{10}\right)-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\left(9+\dfrac{11}{488}\right)-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{125}{22}\times\left(\dfrac{31}{2}+\dfrac{19}{2}+\dfrac{101}{5}\right)\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(\dfrac{31}{4}-11+\dfrac{19}{2}-\dfrac{83}{2}\right)\times\dfrac{31}{4}\times\dfrac{122}{3}\times\left(9\times\left(9+\dfrac{63}{10}\right)-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\left(9+\dfrac{11}{488}\right)-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{125}{22}\times\left(25+\dfrac{101}{5}\right)\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(\dfrac{31}{4}-11+\dfrac{19}{2}-\dfrac{83}{2}\right)\times\dfrac{31}{4}\times\dfrac{122}{3}\times\left(9\times\left(9+\dfrac{63}{10}\right)-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\left(9+\dfrac{11}{488}\right)-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{125}{22}\times\dfrac{226}{5}\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(\dfrac{31}{4}-11+\dfrac{19}{2}-\dfrac{83}{2}\right)\times\dfrac{31}{4}\times\dfrac{122}{3}\times\left(9\times\left(9+\dfrac{63}{10}\right)-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\left(9+\dfrac{11}{488}\right)-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{125}{22}\times\dfrac{226}{5}\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(-\dfrac{13}{4}+\dfrac{19}{2}-\dfrac{83}{2}\right)\times\dfrac{31}{4}\times\dfrac{122}{3}\times\left(9\times\left(9+\dfrac{63}{10}\right)-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\left(9+\dfrac{11}{488}\right)-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{125}{22}\times\dfrac{226}{5}\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(\dfrac{25}{4}-\dfrac{83}{2}\right)\times\dfrac{31}{4}\times\dfrac{122}{3}\times\left(9\times\left(9+\dfrac{63}{10}\right)-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\left(9+\dfrac{11}{488}\right)-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{125}{22}\times\dfrac{226}{5}\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(-\dfrac{141}{4}\right)\times\dfrac{31}{4}\times\dfrac{122}{3}\times\left(9\times\left(9+\dfrac{63}{10}\right)-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\left(9+\dfrac{11}{488}\right)-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{125}{22}\times\dfrac{226}{5}\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(-\dfrac{141}{4}\right)\times\dfrac{1891}{6}\times\left(9\times\left(9+\dfrac{63}{10}\right)-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\left(9+\dfrac{11}{488}\right)-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{125}{22}\times\dfrac{226}{5}\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(-\dfrac{141}{4}\right)\times\dfrac{1891}{6}\times\left(9\times\dfrac{153}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\dfrac{4403}{488}-\dfrac{19}{2}\times\left(-\dfrac{83}{2}\right)+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{125}{22}\times\dfrac{226}{5}\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(-\dfrac{141}{4}\right)\times\dfrac{1891}{6}\times\left(9\times\dfrac{153}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\dfrac{4403}{488}+\dfrac{1577}{4}+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{125}{22}\times\dfrac{226}{5}\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(-\dfrac{141}{4}\right)\times\dfrac{1891}{6}\times\left(9\times\dfrac{153}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\dfrac{4403}{488}+\dfrac{1577}{4}+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11-\left(-\dfrac{2825}{11}\right)\times\dfrac{63}{10}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(-\dfrac{141}{4}\right)\times\dfrac{1891}{6}\times\left(9\times\dfrac{153}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\dfrac{4403}{488}+\dfrac{1577}{4}+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{35595}{22}-9\right)\times\dfrac{122}{3}\times\left(-\dfrac{9}{2}\right)\times12\times\left(-\dfrac{141}{4}\right)\times\dfrac{1891}{6}\times\left(9\times\dfrac{153}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\dfrac{4403}{488}+\dfrac{1577}{4}+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{35595}{22}-9\right)\times\left(-183\right)\times12\times\left(-\dfrac{141}{4}\right)\times\dfrac{1891}{6}\times\left(9\times\dfrac{153}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\dfrac{4403}{488}+\dfrac{1577}{4}+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{35595}{22}-9\right)\times\left(-183\right)\times\left(-423\right)\times\dfrac{1891}{6}\times\left(9\times\dfrac{153}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\dfrac{4403}{488}+\dfrac{1577}{4}+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{35595}{22}-9\right)\times\left(-183\right)\times\left(-\dfrac{266631}{2}\right)\times\left(9\times\dfrac{153}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\dfrac{4403}{488}+\dfrac{1577}{4}+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{35595}{22}-9\right)\times\left(-183\right)\times\left(-\dfrac{266631}{2}\right)\times\left(\dfrac{1377}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\dfrac{196797}{488}+\dfrac{108}{11}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{35595}{22}-9\right)\times\left(-183\right)\times\left(-\dfrac{266631}{2}\right)\times\left(\dfrac{1377}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\left(\dfrac{2217471}{5368}-\dfrac{80}{11}\right)\times\left(\dfrac{80}{11}+11+\dfrac{35595}{22}-9\right)\times\left(-183\right)\times\left(-\dfrac{266631}{2}\right)\times\left(\dfrac{1377}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\dfrac{2178431}{5368}\times\left(\dfrac{80}{11}+11+\dfrac{35595}{22}-9\right)\times\left(-183\right)\times\left(-\dfrac{266631}{2}\right)\times\left(\dfrac{1377}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\dfrac{2178431}{5368}\times\left(\dfrac{201}{11}+\dfrac{35595}{22}-9\right)\times\left(-183\right)\times\left(-\dfrac{266631}{2}\right)\times\left(\dfrac{1377}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\dfrac{2178431}{5368}\times\left(\dfrac{35997}{22}-9\right)\times\left(-183\right)\times\left(-\dfrac{266631}{2}\right)\times\left(\dfrac{1377}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\dfrac{2178431}{5368}\times\dfrac{35799}{22}\times\left(-183\right)\times\left(-\dfrac{266631}{2}\right)\times\left(\dfrac{1377}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\dfrac{2178431}{5368}\times\dfrac{35799}{22}\times\dfrac{48793473}{2}\times\left(\dfrac{1377}{10}-7-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\dfrac{2178431}{5368}\times\dfrac{35799}{22}\times\dfrac{48793473}{2}\times\left(\dfrac{1307}{10}-7\right)\\&=&\left(-11\right)\times\dfrac{122}{3}\times\dfrac{2178431}{5368}\times\dfrac{35799}{22}\times\dfrac{48793473}{2}\times\dfrac{1237}{10}\\&=&\left(-11\right)\times\dfrac{122}{3}\times\dfrac{77985651369}{118096}\times\dfrac{48793473}{2}\times\dfrac{1237}{10}\\&=&\left(-11\right)\times\dfrac{122}{3}\times\dfrac{3805190774460714537}{236192}\times\dfrac{1237}{10}\\&=&\left(-11\right)\times\dfrac{122}{3}\times\dfrac{4.7070209880079E+21}{2361920}\\&=&\left(-\dfrac{1342}{3}\right)\times\dfrac{4.7070209880079E+21}{2361920}\\&=&-\dfrac{6.3168221659066E+24}{7085760}\\ \end{eqnarray*}