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(-\dfrac{54}{7}\right)\sqrt{175}\right)-\dfrac{8}{3}-\left(\left(\dfrac{17}{4}\right)\sqrt{28}\right)+\left(\dfrac{43}{3}\right)\sqrt{49}+\left(\dfrac{17}{4}\right)\sqrt{28}-\dfrac{19}{6}-\dfrac{69}{4}+7+\left(-5\right)\sqrt{63}+\left(-\dfrac{46}{9}\right)\sqrt{63}+\dfrac{55}{4}+\left(-\dfrac{9}{7}\right)\sqrt{28}+\left(-\dfrac{9}{8}\right)\sqrt{49}+\left(\dfrac{18}{7}\right)\sqrt{28}+\left(-\dfrac{61}{7}\right)\sqrt{49}$ et $ Y=\left(\left(\dfrac{31}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{17}{6}\right)\sqrt{175}\right)-\left(\left(\left(2\right)\sqrt{28}\right)-\left(\left(-\dfrac{59}{8}\right)\sqrt{175}\right)-0\right)-\left(\left(4\right)\sqrt{28}\right)-\left(\left(-\dfrac{33}{7}\right)\sqrt{63}+\left(-\dfrac{33}{7}\right)\sqrt{63}+\left(3\right)\sqrt{63}+\left(\dfrac{73}{5}\right)\sqrt{63}+\left(-5\right)\sqrt{175}\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(-\dfrac{54}{7}\right)\sqrt{175}\right)-\dfrac{8}{3}-\left(\left(\dfrac{17}{4}\right)\sqrt{28}\right)+\left(\dfrac{43}{3}\right)\sqrt{49}+\left(\dfrac{17}{4}\right)\sqrt{28}-\dfrac{19}{6}-\dfrac{69}{4}+7+\left(-5\right)\sqrt{63}+\left(-\dfrac{46}{9}\right)\sqrt{63}+\dfrac{55}{4}+\left(-\dfrac{9}{7}\right)\sqrt{28}+\left(-\dfrac{9}{8}\right)\sqrt{49}+\left(\dfrac{18}{7}\right)\sqrt{28}+\left(-\dfrac{61}{7}\right)\sqrt{49}\right)+\left(\left(\left(\dfrac{31}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{17}{6}\right)\sqrt{175}\right)-\left(\left(\left(2\right)\sqrt{28}\right)-\left(\left(-\dfrac{59}{8}\right)\sqrt{175}\right)-0\right)-\left(\left(4\right)\sqrt{28}\right)-\left(\left(-\dfrac{33}{7}\right)\sqrt{63}+\left(-\dfrac{33}{7}\right)\sqrt{63}+\left(3\right)\sqrt{63}+\left(\dfrac{73}{5}\right)\sqrt{63}+\left(-5\right)\sqrt{175}\right)\right)\\ &=&\left(\left(\left(-\dfrac{270}{7}\right)\sqrt{7}\right)-\dfrac{8}{3}-\left(\left(\dfrac{17}{2}\right)\sqrt{7}\right)+\dfrac{301}{3}+\left(\dfrac{17}{2}\right)\sqrt{7}-\dfrac{19}{6}-\dfrac{69}{4}+7+\left(-15\right)\sqrt{7}+\left(-\dfrac{46}{3}\right)\sqrt{7}+\dfrac{55}{4}+\left(-\dfrac{18}{7}\right)\sqrt{7}-\dfrac{63}{8}+\left(\dfrac{36}{7}\right)\sqrt{7}-61\right)+\left(\left(\left(31\right)\sqrt{7}\right)-\left(\left(\dfrac{85}{6}\right)\sqrt{7}\right)-\left(\left(\left(4\right)\sqrt{7}\right)-\left(\left(-\dfrac{295}{8}\right)\sqrt{7}\right)-0\right)-\left(\left(8\right)\sqrt{7}\right)-\left(\left(-\dfrac{99}{7}\right)\sqrt{7}+\left(-\dfrac{99}{7}\right)\sqrt{7}+\left(9\right)\sqrt{7}+\left(\dfrac{219}{5}\right)\sqrt{7}+\left(-25\right)\sqrt{7}\right)\right)\\ &=&\left(\left(-\dfrac{270}{7}\right)\sqrt{7}\right)-\dfrac{8}{3}-\left(\left(\dfrac{17}{2}\right)\sqrt{7}\right)+\dfrac{301}{3}+\left(\dfrac{17}{2}\right)\sqrt{7}-\dfrac{19}{6}-\dfrac{69}{4}+7+\left(-15\right)\sqrt{7}+\left(-\dfrac{46}{3}\right)\sqrt{7}+\dfrac{55}{4}+\left(-\dfrac{18}{7}\right)\sqrt{7}-\dfrac{63}{8}+\left(\dfrac{36}{7}\right)\sqrt{7}-61+\left(\left(31\right)\sqrt{7}\right)-\left(\left(\dfrac{85}{6}\right)\sqrt{7}\right)-\left(\left(\left(4\right)\sqrt{7}\right)-\left(\left(-\dfrac{295}{8}\right)\sqrt{7}\right)-0\right)-\left(\left(8\right)\sqrt{7}\right)-\left(\left(-\dfrac{99}{7}\right)\sqrt{7}+\left(-\dfrac{99}{7}\right)\sqrt{7}+\left(9\right)\sqrt{7}+\left(\dfrac{219}{5}\right)\sqrt{7}+\left(-25\right)\sqrt{7}\right)\\ &=&\left(-\dfrac{27409}{280}\right)\sqrt{7}+\dfrac{233}{8}\\ \end{eqnarray*} \begin{eqnarray*} X-Y &=&\left(\left(\left(-\dfrac{54}{7}\right)\sqrt{175}\right)-\dfrac{8}{3}-\left(\left(\dfrac{17}{4}\right)\sqrt{28}\right)+\left(\dfrac{43}{3}\right)\sqrt{49}+\left(\dfrac{17}{4}\right)\sqrt{28}-\dfrac{19}{6}-\dfrac{69}{4}+7+\left(-5\right)\sqrt{63}+\left(-\dfrac{46}{9}\right)\sqrt{63}+\dfrac{55}{4}+\left(-\dfrac{9}{7}\right)\sqrt{28}+\left(-\dfrac{9}{8}\right)\sqrt{49}+\left(\dfrac{18}{7}\right)\sqrt{28}+\left(-\dfrac{61}{7}\right)\sqrt{49}\right)-\left(\left(\left(\dfrac{31}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{17}{6}\right)\sqrt{175}\right)-\left(\left(\left(2\right)\sqrt{28}\right)-\left(\left(-\dfrac{59}{8}\right)\sqrt{175}\right)-0\right)-\left(\left(4\right)\sqrt{28}\right)-\left(\left(-\dfrac{33}{7}\right)\sqrt{63}+\left(-\dfrac{33}{7}\right)\sqrt{63}+\left(3\right)\sqrt{63}+\left(\dfrac{73}{5}\right)\sqrt{63}+\left(-5\right)\sqrt{175}\right)\right)\\ &=&\left(\left(\left(-\dfrac{270}{7}\right)\sqrt{7}\right)-\dfrac{8}{3}-\left(\left(\dfrac{17}{2}\right)\sqrt{7}\right)+\dfrac{301}{3}+\left(\dfrac{17}{2}\right)\sqrt{7}-\dfrac{19}{6}-\dfrac{69}{4}+7+\left(-15\right)\sqrt{7}+\left(-\dfrac{46}{3}\right)\sqrt{7}+\dfrac{55}{4}+\left(-\dfrac{18}{7}\right)\sqrt{7}-\dfrac{63}{8}+\left(\dfrac{36}{7}\right)\sqrt{7}-61\right)-\left(\left(\left(31\right)\sqrt{7}\right)-\left(\left(\dfrac{85}{6}\right)\sqrt{7}\right)-\left(\left(\left(4\right)\sqrt{7}\right)-\left(\left(-\dfrac{295}{8}\right)\sqrt{7}\right)-0\right)-\left(\left(8\right)\sqrt{7}\right)-\left(\left(-\dfrac{99}{7}\right)\sqrt{7}+\left(-\dfrac{99}{7}\right)\sqrt{7}+\left(9\right)\sqrt{7}+\left(\dfrac{219}{5}\right)\sqrt{7}+\left(-25\right)\sqrt{7}\right)\right)\\ &=&\left(\left(-\dfrac{199}{3}\right)\sqrt{7}+\dfrac{233}{8}\right)-\left(\left(-\dfrac{26507}{840}\right)\sqrt{7}+0\right)\\ &=&\left(-\dfrac{199}{3}\right)\sqrt{7}+\dfrac{233}{8}+\left(\dfrac{26507}{840}\right)\sqrt{7}+0\\ &=&\left(-\dfrac{29213}{840}\right)\sqrt{7}+\dfrac{233}{8}\\ \end{eqnarray*} \begin{eqnarray*} X\times Y &=&\left(\left(\left(-\dfrac{54}{7}\right)\sqrt{175}\right)-\dfrac{8}{3}-\left(\left(\dfrac{17}{4}\right)\sqrt{28}\right)+\left(\dfrac{43}{3}\right)\sqrt{49}+\left(\dfrac{17}{4}\right)\sqrt{28}-\dfrac{19}{6}-\dfrac{69}{4}+7+\left(-5\right)\sqrt{63}+\left(-\dfrac{46}{9}\right)\sqrt{63}+\dfrac{55}{4}+\left(-\dfrac{9}{7}\right)\sqrt{28}+\left(-\dfrac{9}{8}\right)\sqrt{49}+\left(\dfrac{18}{7}\right)\sqrt{28}+\left(-\dfrac{61}{7}\right)\sqrt{49}\right)\times\left(\left(\left(\dfrac{31}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{17}{6}\right)\sqrt{175}\right)-\left(\left(\left(2\right)\sqrt{28}\right)-\left(\left(-\dfrac{59}{8}\right)\sqrt{175}\right)-0\right)-\left(\left(4\right)\sqrt{28}\right)-\left(\left(-\dfrac{33}{7}\right)\sqrt{63}+\left(-\dfrac{33}{7}\right)\sqrt{63}+\left(3\right)\sqrt{63}+\left(\dfrac{73}{5}\right)\sqrt{63}+\left(-5\right)\sqrt{175}\right)\right)\\ &=&\left(\left(\left(-\dfrac{270}{7}\right)\sqrt{7}\right)-\dfrac{8}{3}-\left(\left(\dfrac{17}{2}\right)\sqrt{7}\right)+\dfrac{301}{3}+\left(\dfrac{17}{2}\right)\sqrt{7}-\dfrac{19}{6}-\dfrac{69}{4}+7+\left(-15\right)\sqrt{7}+\left(-\dfrac{46}{3}\right)\sqrt{7}+\dfrac{55}{4}+\left(-\dfrac{18}{7}\right)\sqrt{7}-\dfrac{63}{8}+\left(\dfrac{36}{7}\right)\sqrt{7}-61\right)\times\left(\left(\left(31\right)\sqrt{7}\right)-\left(\left(\dfrac{85}{6}\right)\sqrt{7}\right)-\left(\left(\left(4\right)\sqrt{7}\right)-\left(\left(-\dfrac{295}{8}\right)\sqrt{7}\right)-0\right)-\left(\left(8\right)\sqrt{7}\right)-\left(\left(-\dfrac{99}{7}\right)\sqrt{7}+\left(-\dfrac{99}{7}\right)\sqrt{7}+\left(9\right)\sqrt{7}+\left(\dfrac{219}{5}\right)\sqrt{7}+\left(-25\right)\sqrt{7}\right)\right)\\ &=&\left(\left(-\dfrac{199}{3}\right)\sqrt{7}+\dfrac{233}{8}\right)\left(\left(-\dfrac{26507}{840}\right)\sqrt{7}+0\right)\\ &=&\left(\dfrac{5274893}{2520}\right)\sqrt{49}+\left(-\dfrac{6176131}{6720}\right)\sqrt{7}+0\\ &=&\dfrac{5274893}{360}+\left(-\dfrac{6176131}{6720}\right)\sqrt{7}\\ \end{eqnarray*}