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

Soit $ X=\left(\left(\left(0\right)\sqrt{18}\right)-\left(\left(0\right)\sqrt{50}\right)-\left(\left(-3\right)\sqrt{8}\right)-\left(\left(0\right)\sqrt{50}\right)\right)-\left(\left(\left(0\right)\sqrt{18}\right)-\left(\left(\dfrac{20}{9}\right)\sqrt{8}\right)-\left(\left(6\right)\sqrt{4}\right)\right)$ et $ Y=\left(\left(-\dfrac{15}{7}\right)\sqrt{18}\right)-\left(0-\left(\left(-9\right)\sqrt{18}\right)-\left(\left(\dfrac{59}{2}\right)\sqrt{4}\right)-9\right)-\left(\left(-\dfrac{15}{4}\right)\sqrt{18}+\left(\dfrac{37}{2}\right)\sqrt{4}+\left(8\right)\sqrt{18}+\left(-\dfrac{53}{3}\right)\sqrt{50}\right)-\left(\left(\left(\dfrac{64}{7}\right)\sqrt{50}\right)+\dfrac{3}{7}-\left(\left(-\dfrac{53}{3}\right)\sqrt{50}\right)-\left(\left(\dfrac{79}{4}\right)\sqrt{4}\right)\right)$ . Calculer et simplifier $ X+Y$ , $ X-Y$ et $ X\times Y$ .

Cliquer ici pour afficher la solution

Exercice

\begin{eqnarray*} X+Y &=&\left(\left(\left(\left(0\right)\sqrt{18}\right)-\left(\left(0\right)\sqrt{50}\right)-\left(\left(-3\right)\sqrt{8}\right)-\left(\left(0\right)\sqrt{50}\right)\right)-\left(\left(\left(0\right)\sqrt{18}\right)-\left(\left(\dfrac{20}{9}\right)\sqrt{8}\right)-\left(\left(6\right)\sqrt{4}\right)\right)\right)+\left(\left(\left(-\dfrac{15}{7}\right)\sqrt{18}\right)-\left(0-\left(\left(-9\right)\sqrt{18}\right)-\left(\left(\dfrac{59}{2}\right)\sqrt{4}\right)-9\right)-\left(\left(-\dfrac{15}{4}\right)\sqrt{18}+\left(\dfrac{37}{2}\right)\sqrt{4}+\left(8\right)\sqrt{18}+\left(-\dfrac{53}{3}\right)\sqrt{50}\right)-\left(\left(\left(\dfrac{64}{7}\right)\sqrt{50}\right)+\dfrac{3}{7}-\left(\left(-\dfrac{53}{3}\right)\sqrt{50}\right)-\left(\left(\dfrac{79}{4}\right)\sqrt{4}\right)\right)\right)\\ &=&\left(\left(\left(\left(0\right)\sqrt{2}\right)-\left(\left(0\right)\sqrt{2}\right)-\left(\left(-6\right)\sqrt{2}\right)-\left(\left(0\right)\sqrt{2}\right)\right)-\left(\left(\left(0\right)\sqrt{2}\right)-\left(\left(\dfrac{40}{9}\right)\sqrt{2}\right)-12\right)\right)+\left(\left(\left(-\dfrac{45}{7}\right)\sqrt{2}\right)-\left(0-\left(\left(-27\right)\sqrt{2}\right)-59-9\right)-\left(\left(-\dfrac{45}{4}\right)\sqrt{2}+37+\left(24\right)\sqrt{2}+\left(-\dfrac{265}{3}\right)\sqrt{2}\right)-\left(\left(\left(\dfrac{320}{7}\right)\sqrt{2}\right)+\dfrac{3}{7}-\left(\left(-\dfrac{265}{3}\right)\sqrt{2}\right)-\dfrac{79}{2}\right)\right)\\ &=&\left(\left(\left(0\right)\sqrt{2}\right)-\left(\left(0\right)\sqrt{2}\right)-\left(\left(-6\right)\sqrt{2}\right)-\left(\left(0\right)\sqrt{2}\right)\right)-\left(\left(\left(0\right)\sqrt{2}\right)-\left(\left(\dfrac{40}{9}\right)\sqrt{2}\right)-12\right)+\left(\left(-\dfrac{45}{7}\right)\sqrt{2}\right)-\left(0-\left(\left(-27\right)\sqrt{2}\right)-59-9\right)-\left(\left(-\dfrac{45}{4}\right)\sqrt{2}+37+\left(24\right)\sqrt{2}+\left(-\dfrac{265}{3}\right)\sqrt{2}\right)-\left(\left(\left(\dfrac{320}{7}\right)\sqrt{2}\right)+\dfrac{3}{7}-\left(\left(-\dfrac{265}{3}\right)\sqrt{2}\right)-\dfrac{79}{2}\right)\\ &=&\left(-\dfrac{20525}{252}\right)\sqrt{2}+\dfrac{1149}{14}\\ \end{eqnarray*} \begin{eqnarray*} X-Y &=&\left(\left(\left(\left(0\right)\sqrt{18}\right)-\left(\left(0\right)\sqrt{50}\right)-\left(\left(-3\right)\sqrt{8}\right)-\left(\left(0\right)\sqrt{50}\right)\right)-\left(\left(\left(0\right)\sqrt{18}\right)-\left(\left(\dfrac{20}{9}\right)\sqrt{8}\right)-\left(\left(6\right)\sqrt{4}\right)\right)\right)-\left(\left(\left(-\dfrac{15}{7}\right)\sqrt{18}\right)-\left(0-\left(\left(-9\right)\sqrt{18}\right)-\left(\left(\dfrac{59}{2}\right)\sqrt{4}\right)-9\right)-\left(\left(-\dfrac{15}{4}\right)\sqrt{18}+\left(\dfrac{37}{2}\right)\sqrt{4}+\left(8\right)\sqrt{18}+\left(-\dfrac{53}{3}\right)\sqrt{50}\right)-\left(\left(\left(\dfrac{64}{7}\right)\sqrt{50}\right)+\dfrac{3}{7}-\left(\left(-\dfrac{53}{3}\right)\sqrt{50}\right)-\left(\left(\dfrac{79}{4}\right)\sqrt{4}\right)\right)\right)\\ &=&\left(\left(\left(\left(0\right)\sqrt{2}\right)-\left(\left(0\right)\sqrt{2}\right)-\left(\left(-6\right)\sqrt{2}\right)-\left(\left(0\right)\sqrt{2}\right)\right)-\left(\left(\left(0\right)\sqrt{2}\right)-\left(\left(\dfrac{40}{9}\right)\sqrt{2}\right)-12\right)\right)-\left(\left(\left(-\dfrac{45}{7}\right)\sqrt{2}\right)-\left(0-\left(\left(-27\right)\sqrt{2}\right)-59-9\right)-\left(\left(-\dfrac{45}{4}\right)\sqrt{2}+37+\left(24\right)\sqrt{2}+\left(-\dfrac{265}{3}\right)\sqrt{2}\right)-\left(\left(\left(\dfrac{320}{7}\right)\sqrt{2}\right)+\dfrac{3}{7}-\left(\left(-\dfrac{265}{3}\right)\sqrt{2}\right)-\dfrac{79}{2}\right)\right)\\ &=&\left(\left(\dfrac{94}{9}\right)\sqrt{2}+12\right)-\left(\left(-\dfrac{2573}{28}\right)\sqrt{2}+\dfrac{981}{14}\right)\\ &=&\left(\dfrac{94}{9}\right)\sqrt{2}+12+\left(\dfrac{2573}{28}\right)\sqrt{2}-\dfrac{981}{14}\\ &=&\left(\dfrac{25789}{252}\right)\sqrt{2}-\dfrac{813}{14}\\ \end{eqnarray*} \begin{eqnarray*} X\times Y &=&\left(\left(\left(\left(0\right)\sqrt{18}\right)-\left(\left(0\right)\sqrt{50}\right)-\left(\left(-3\right)\sqrt{8}\right)-\left(\left(0\right)\sqrt{50}\right)\right)-\left(\left(\left(0\right)\sqrt{18}\right)-\left(\left(\dfrac{20}{9}\right)\sqrt{8}\right)-\left(\left(6\right)\sqrt{4}\right)\right)\right)\times\left(\left(\left(-\dfrac{15}{7}\right)\sqrt{18}\right)-\left(0-\left(\left(-9\right)\sqrt{18}\right)-\left(\left(\dfrac{59}{2}\right)\sqrt{4}\right)-9\right)-\left(\left(-\dfrac{15}{4}\right)\sqrt{18}+\left(\dfrac{37}{2}\right)\sqrt{4}+\left(8\right)\sqrt{18}+\left(-\dfrac{53}{3}\right)\sqrt{50}\right)-\left(\left(\left(\dfrac{64}{7}\right)\sqrt{50}\right)+\dfrac{3}{7}-\left(\left(-\dfrac{53}{3}\right)\sqrt{50}\right)-\left(\left(\dfrac{79}{4}\right)\sqrt{4}\right)\right)\right)\\ &=&\left(\left(\left(\left(0\right)\sqrt{2}\right)-\left(\left(0\right)\sqrt{2}\right)-\left(\left(-6\right)\sqrt{2}\right)-\left(\left(0\right)\sqrt{2}\right)\right)-\left(\left(\left(0\right)\sqrt{2}\right)-\left(\left(\dfrac{40}{9}\right)\sqrt{2}\right)-12\right)\right)\times\left(\left(\left(-\dfrac{45}{7}\right)\sqrt{2}\right)-\left(0-\left(\left(-27\right)\sqrt{2}\right)-59-9\right)-\left(\left(-\dfrac{45}{4}\right)\sqrt{2}+37+\left(24\right)\sqrt{2}+\left(-\dfrac{265}{3}\right)\sqrt{2}\right)-\left(\left(\left(\dfrac{320}{7}\right)\sqrt{2}\right)+\dfrac{3}{7}-\left(\left(-\dfrac{265}{3}\right)\sqrt{2}\right)-\dfrac{79}{2}\right)\right)\\ &=&\left(\left(\dfrac{94}{9}\right)\sqrt{2}+12\right)\left(\left(-\dfrac{2573}{28}\right)\sqrt{2}+\dfrac{981}{14}\right)\\ &=&\left(-\dfrac{120931}{126}\right)\sqrt{4}+\left(-\dfrac{2596}{7}\right)\sqrt{2}+\dfrac{5886}{7}\\ &=&-\dfrac{67957}{63}+\left(-\dfrac{2596}{7}\right)\sqrt{2}\\ \end{eqnarray*}