Ataraxy

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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 \[-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(\dfrac{6}{11}-\left(\left(-1\right)\times\left(-13\right)\times\dfrac{161}{11}\times\dfrac{54}{19}\times\dfrac{43}{18}-\left(-17\right)\times\dfrac{161}{11}\times\left(-5\right)\times7\times\left(-\dfrac{71}{5}\right)\right)+\dfrac{193}{7}-\dfrac{-\dfrac{193}{7}}{\dfrac{\dfrac{14}{8}}{\dfrac{171}{5}}}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(\dfrac{6}{11}-\left(\left(-1\right)\times\left(-13\right)\times\dfrac{161}{11}\times\dfrac{54}{19}\times\dfrac{43}{18}-\left(-17\right)\times\dfrac{161}{11}\times\left(-5\right)\times7\times\left(-\dfrac{71}{5}\right)\right)+\dfrac{193}{7}-\dfrac{-\dfrac{193}{7}}{\dfrac{\dfrac{14}{8}}{\dfrac{171}{5}}}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}=-\dfrac{3.276690608179E+24}{16601057327212050}$ . Voici le détail : \begin{eqnarray*} X &=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(\dfrac{6}{11}-\left(13\times\dfrac{161}{11}\times\dfrac{54}{19}\times\dfrac{43}{18}-\left(-17\right)\times\dfrac{161}{11}\times\left(-5\right)\times7\times\left(-\dfrac{71}{5}\right)\right)+\dfrac{193}{7}-\dfrac{-\dfrac{193}{7}}{\dfrac{\dfrac{14}{8}}{\dfrac{171}{5}}}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(\dfrac{6}{11}-\left(\dfrac{2093}{11}\times\dfrac{54}{19}\times\dfrac{43}{18}-\left(-17\right)\times\dfrac{161}{11}\times\left(-5\right)\times7\times\left(-\dfrac{71}{5}\right)\right)+\dfrac{193}{7}-\dfrac{-\dfrac{193}{7}}{\dfrac{\dfrac{14}{8}}{\dfrac{171}{5}}}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(\dfrac{6}{11}-\left(\dfrac{113022}{209}\times\dfrac{43}{18}-\left(-17\right)\times\dfrac{161}{11}\times\left(-5\right)\times7\times\left(-\dfrac{71}{5}\right)\right)+\dfrac{193}{7}-\dfrac{-\dfrac{193}{7}}{\dfrac{\dfrac{14}{8}}{\dfrac{171}{5}}}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(\dfrac{6}{11}-\left(\dfrac{269997}{209}-\left(-17\right)\times\dfrac{161}{11}\times\left(-5\right)\times7\times\left(-\dfrac{71}{5}\right)\right)+\dfrac{193}{7}-\dfrac{-\dfrac{193}{7}}{\dfrac{\dfrac{14}{8}}{\dfrac{171}{5}}}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(\dfrac{6}{11}-\left(\dfrac{269997}{209}-\left(-\dfrac{2737}{11}\right)\times\left(-5\right)\times7\times\left(-\dfrac{71}{5}\right)\right)+\dfrac{193}{7}-\dfrac{-\dfrac{193}{7}}{\dfrac{\dfrac{14}{8}}{\dfrac{171}{5}}}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(\dfrac{6}{11}-\left(\dfrac{269997}{209}-\dfrac{13685}{11}\times7\times\left(-\dfrac{71}{5}\right)\right)+\dfrac{193}{7}-\dfrac{-\dfrac{193}{7}}{\dfrac{\dfrac{14}{8}}{\dfrac{171}{5}}}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(\dfrac{6}{11}-\left(\dfrac{269997}{209}-\dfrac{95795}{11}\times\left(-\dfrac{71}{5}\right)\right)+\dfrac{193}{7}-\dfrac{-\dfrac{193}{7}}{\dfrac{\dfrac{14}{8}}{\dfrac{171}{5}}}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(\dfrac{6}{11}-\left(\dfrac{269997}{209}+\dfrac{1360289}{11}\right)+\dfrac{193}{7}-\dfrac{-\dfrac{193}{7}}{\dfrac{\dfrac{14}{8}}{\dfrac{171}{5}}}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(\dfrac{6}{11}-\left(\dfrac{269997}{209}+\dfrac{1360289}{11}\right)+\dfrac{193}{7}-\dfrac{-\dfrac{193}{7}}{\dfrac{\dfrac{7}{4}}{\dfrac{171}{5}}}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(\dfrac{6}{11}-\left(\dfrac{269997}{209}+\dfrac{1360289}{11}\right)+\dfrac{193}{7}-\dfrac{-\dfrac{193}{7}}{\dfrac{35}{684}}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(\dfrac{6}{11}-\dfrac{26115488}{209}+\dfrac{193}{7}-\dfrac{-\dfrac{193}{7}}{\dfrac{35}{684}}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(\dfrac{6}{11}-\dfrac{26115488}{209}+\dfrac{193}{7}+\dfrac{132012}{245}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(-\dfrac{26115374}{209}+\dfrac{193}{7}+\dfrac{132012}{245}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(-\dfrac{182767281}{1463}+\dfrac{132012}{245}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}-\left(-\dfrac{44584850289}{358435}-8\right)-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}+\dfrac{44587717769}{358435}-\dfrac{\dfrac{\dfrac{7}{-5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}+\dfrac{44587717769}{358435}-\dfrac{\dfrac{-\dfrac{7}{5}}{-1}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}+\dfrac{44587717769}{358435}-\dfrac{\dfrac{7}{5}}{\dfrac{318}{7}}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{80}{7}+\dfrac{44587717769}{358435}-\dfrac{49}{1590}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{312142699183}{2509045}-\dfrac{49}{1590}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\left(\dfrac{496306768757765}{3989381550}-7\right)\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\dfrac{496278843086915}{3989381550}\times\dfrac{161}{11}\times\left(\dfrac{6}{11}+\dfrac{335}{17}\right)\times\dfrac{91}{17}\\&=&-13-\left(\dfrac{318}{7}+\dfrac{91}{17}\right)-\dfrac{496278843086915}{3989381550}\times\dfrac{161}{11}\times\dfrac{3787}{187}\times\dfrac{91}{17}\\&=&-13-\dfrac{6043}{119}-\dfrac{496278843086915}{3989381550}\times\dfrac{161}{11}\times\dfrac{3787}{187}\times\dfrac{91}{17}\\&=&-13-\dfrac{6043}{119}-\dfrac{79900893736993315}{43883197050}\times\dfrac{3787}{187}\times\dfrac{91}{17}\\&=&-13-\dfrac{6043}{119}-\dfrac{3.0258468458199E+20}{8206157848350}\times\dfrac{91}{17}\\&=&-13-\dfrac{6043}{119}-\dfrac{2.7535206296961E+22}{139504683421950}\\&=&-\dfrac{7590}{119}-\dfrac{2.7535206296961E+22}{139504683421950}\\&=&-\dfrac{3.276690608179E+24}{16601057327212050}\\ \end{eqnarray*}