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 \[-5-\left(-11\right)\times\dfrac{103}{4}\times\left(-5\right)\times\left(-5+\dfrac{26}{7}\right)\times\left(-\dfrac{43}{10}\right)\times\left(-\dfrac{27}{2}-\left(5-5-5\right)-\left(-5\right)\times5\times\left(-5\right)\right)\times\left(\left(-6\right)\times\dfrac{26}{7}\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-\left(5-5+5\right)-\dfrac{52}{9}}}{-11}\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=-5-\left(-11\right)\times\dfrac{103}{4}\times\left(-5\right)\times\left(-5+\dfrac{26}{7}\right)\times\left(-\dfrac{43}{10}\right)\times\left(-\dfrac{27}{2}-\left(5-5-5\right)-\left(-5\right)\times5\times\left(-5\right)\right)\times\left(\left(-6\right)\times\dfrac{26}{7}\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-\left(5-5+5\right)-\dfrac{52}{9}}}{-11}=-\dfrac{1986122365345}{1568}$ . Voici le détail : \begin{eqnarray*} X &=&-5-\left(-\dfrac{1133}{4}\right)\times\left(-5\right)\times\left(-5+\dfrac{26}{7}\right)\times\left(-\dfrac{43}{10}\right)\times\left(-\dfrac{27}{2}-\left(5-5-5\right)-\left(-5\right)\times5\times\left(-5\right)\right)\times\left(\left(-6\right)\times\dfrac{26}{7}\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-\left(5-5+5\right)-\dfrac{52}{9}}}{-11}\\&=&-5-\left(-\dfrac{1133}{4}\right)\times\left(-5\right)\times-\dfrac{9}{7}\times\left(-\dfrac{43}{10}\right)\times\left(-\dfrac{27}{2}-\left(5-5-5\right)-\left(-5\right)\times5\times\left(-5\right)\right)\times\left(\left(-6\right)\times\dfrac{26}{7}\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-\left(5-5+5\right)-\dfrac{52}{9}}}{-11}\\&=&-5-\left(-\dfrac{1133}{4}\right)\times\left(-5\right)\times-\dfrac{9}{7}\times\left(-\dfrac{43}{10}\right)\times\left(-\dfrac{27}{2}-\left(0-5\right)-\left(-5\right)\times5\times\left(-5\right)\right)\times\left(\left(-6\right)\times\dfrac{26}{7}\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-\left(5-5+5\right)-\dfrac{52}{9}}}{-11}\\&=&-5-\left(-\dfrac{1133}{4}\right)\times\left(-5\right)\times-\dfrac{9}{7}\times\left(-\dfrac{43}{10}\right)\times\left(-\dfrac{27}{2}+5-\left(-5\right)\times5\times\left(-5\right)\right)\times\left(\left(-6\right)\times\dfrac{26}{7}\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-\left(5-5+5\right)-\dfrac{52}{9}}}{-11}\\&=&-5-\left(-\dfrac{1133}{4}\right)\times\left(-5\right)\times-\dfrac{9}{7}\times\left(-\dfrac{43}{10}\right)\times\left(-\dfrac{27}{2}+5-\left(-25\right)\times\left(-5\right)\right)\times\left(\left(-6\right)\times\dfrac{26}{7}\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-\left(5-5+5\right)-\dfrac{52}{9}}}{-11}\\&=&-5-\left(-\dfrac{1133}{4}\right)\times\left(-5\right)\times-\dfrac{9}{7}\times\left(-\dfrac{43}{10}\right)\times\left(-\dfrac{27}{2}+5-125\right)\times\left(\left(-6\right)\times\dfrac{26}{7}\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-\left(5-5+5\right)-\dfrac{52}{9}}}{-11}\\&=&-5-\left(-\dfrac{1133}{4}\right)\times\left(-5\right)\times-\dfrac{9}{7}\times\left(-\dfrac{43}{10}\right)\times\left(-\dfrac{27}{2}+5-125\right)\times\left(\left(-6\right)\times\dfrac{26}{7}\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-\left(5-5+5\right)-\dfrac{52}{9}}}{-11}\\&=&-5-\left(-\dfrac{1133}{4}\right)\times\left(-5\right)\times-\dfrac{9}{7}\times\left(-\dfrac{43}{10}\right)\times\left(-\dfrac{27}{2}+5-125\right)\times\left(\left(-6\right)\times\dfrac{26}{7}\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-\left(0+5\right)-\dfrac{52}{9}}}{-11}\\&=&-5-\left(-\dfrac{1133}{4}\right)\times\left(-5\right)\times-\dfrac{9}{7}\times\left(-\dfrac{43}{10}\right)\times\left(-\dfrac{27}{2}+5-125\right)\times\left(\left(-6\right)\times\dfrac{26}{7}\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-5-\dfrac{52}{9}}}{-11}\\&=&-5-\dfrac{5665}{4}\times-\dfrac{9}{7}\times\left(-\dfrac{43}{10}\right)\times\left(-\dfrac{27}{2}+5-125\right)\times\left(\left(-6\right)\times\dfrac{26}{7}\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-5-\dfrac{52}{9}}}{-11}\\&=&-5+\dfrac{50985}{28}\times\left(-\dfrac{43}{10}\right)\times\left(-\dfrac{27}{2}+5-125\right)\times\left(\left(-6\right)\times\dfrac{26}{7}\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-5-\dfrac{52}{9}}}{-11}\\&=&-5+\dfrac{50985}{28}\times\left(-\dfrac{43}{10}\right)\times\left(-\dfrac{17}{2}-125\right)\times\left(\left(-6\right)\times\dfrac{26}{7}\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-5-\dfrac{52}{9}}}{-11}\\&=&-5+\dfrac{50985}{28}\times\left(-\dfrac{43}{10}\right)\times-\dfrac{267}{2}\times\left(\left(-6\right)\times\dfrac{26}{7}\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-5-\dfrac{52}{9}}}{-11}\\&=&-5+\dfrac{50985}{28}\times\left(-\dfrac{43}{10}\right)\times-\dfrac{267}{2}\times\left(\left(-\dfrac{156}{7}\right)\times10-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-5-\dfrac{52}{9}}}{-11}\\&=&-5+\dfrac{50985}{28}\times\left(-\dfrac{43}{10}\right)\times-\dfrac{267}{2}\times\left(-\dfrac{1560}{7}-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}+\dfrac{1}{4}-5-\dfrac{52}{9}}}{-11}\\&=&-5+\dfrac{50985}{28}\times\left(-\dfrac{43}{10}\right)\times-\dfrac{267}{2}\times\left(-\dfrac{1560}{7}-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}-\dfrac{19}{4}-\dfrac{52}{9}}}{-11}\\&=&-5+\dfrac{50985}{28}\times\left(-\dfrac{43}{10}\right)\times-\dfrac{267}{2}\times\left(-\dfrac{1560}{7}-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}-\dfrac{379}{36}}}{-11}\\&=&-5-\dfrac{438471}{56}\times-\dfrac{267}{2}\times\left(-\dfrac{1560}{7}-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}-\dfrac{379}{36}}}{-11}\\&=&-5+\dfrac{117071757}{112}\times\left(-\dfrac{1560}{7}-6-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}-\dfrac{379}{36}}}{-11}\\&=&-5+\dfrac{117071757}{112}\times\left(-\dfrac{1602}{7}-\dfrac{27}{2}\right)\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}-\dfrac{379}{36}}}{-11}\\&=&-5+\dfrac{117071757}{112}\times-\dfrac{3393}{14}\times5-\dfrac{\dfrac{4-5+1}{\dfrac{103}{4}-\dfrac{379}{36}}}{-11}\\&=&-5+\dfrac{117071757}{112}\times-\dfrac{3393}{14}\times5-\dfrac{\dfrac{-1+1}{\dfrac{103}{4}-\dfrac{379}{36}}}{-11}\\&=&-5+\dfrac{117071757}{112}\times-\dfrac{3393}{14}\times5-\dfrac{\dfrac{0}{\dfrac{103}{4}-\dfrac{379}{36}}}{-11}\\&=&-5+\dfrac{117071757}{112}\times-\dfrac{3393}{14}\times5-\dfrac{\dfrac{0}{\dfrac{137}{9}}}{-11}\\&=&-5-\dfrac{397224471501}{1568}\times5-\dfrac{\dfrac{0}{\dfrac{137}{9}}}{-11}\\&=&-5-\dfrac{1986122357505}{1568}-\dfrac{\dfrac{0}{\dfrac{137}{9}}}{-11}\\&=&-5-\dfrac{1986122357505}{1568}-\dfrac{0}{-11}\\&=&-5-\dfrac{1986122357505}{1568}-0\\&=&-\dfrac{1986122365345}{1568}-0\\&=&-\dfrac{1986122365345}{1568}\\ \end{eqnarray*}