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{14}{5}\right)\sqrt{28}\right)-\left(\left(2\right)\sqrt{175}+\left(\dfrac{53}{2}\right)\sqrt{63}+\left(\dfrac{51}{4}\right)\sqrt{63}+\left(\dfrac{40}{9}\right)\sqrt{28}\right)$ et $ Y=\left(\left(\dfrac{14}{3}\right)\sqrt{49}+\left(\dfrac{7}{2}\right)\sqrt{63}+\left(1\right)\sqrt{175}+\left(\dfrac{44}{3}\right)\sqrt{49}\right)-\left(\left(\left(\dfrac{9}{4}\right)\sqrt{28}\right)-\left(\left(-\dfrac{53}{4}\right)\sqrt{49}\right)\right)-\left(\left(-7\right)\sqrt{175}+\dfrac{3}{2}+\left(\dfrac{7}{2}\right)\sqrt{63}+\left(-\dfrac{47}{2}\right)\sqrt{63}\right)-\left(\left(\left(-\dfrac{23}{4}\right)\sqrt{28}\right)-\left(\left(-\dfrac{10}{7}\right)\sqrt{175}\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(-\dfrac{14}{5}\right)\sqrt{28}\right)-\left(\left(2\right)\sqrt{175}+\left(\dfrac{53}{2}\right)\sqrt{63}+\left(\dfrac{51}{4}\right)\sqrt{63}+\left(\dfrac{40}{9}\right)\sqrt{28}\right)\right)+\left(\left(\left(\dfrac{14}{3}\right)\sqrt{49}+\left(\dfrac{7}{2}\right)\sqrt{63}+\left(1\right)\sqrt{175}+\left(\dfrac{44}{3}\right)\sqrt{49}\right)-\left(\left(\left(\dfrac{9}{4}\right)\sqrt{28}\right)-\left(\left(-\dfrac{53}{4}\right)\sqrt{49}\right)\right)-\left(\left(-7\right)\sqrt{175}+\dfrac{3}{2}+\left(\dfrac{7}{2}\right)\sqrt{63}+\left(-\dfrac{47}{2}\right)\sqrt{63}\right)-\left(\left(\left(-\dfrac{23}{4}\right)\sqrt{28}\right)-\left(\left(-\dfrac{10}{7}\right)\sqrt{175}\right)\right)\right)\\ &=&\left(\left(\left(-\dfrac{28}{5}\right)\sqrt{7}\right)-\left(\left(10\right)\sqrt{7}+\left(\dfrac{159}{2}\right)\sqrt{7}+\left(\dfrac{153}{4}\right)\sqrt{7}+\left(\dfrac{80}{9}\right)\sqrt{7}\right)\right)+\left(\left(\dfrac{98}{3}+\left(\dfrac{21}{2}\right)\sqrt{7}+\left(5\right)\sqrt{7}+\dfrac{308}{3}\right)-\left(\left(\left(\dfrac{9}{2}\right)\sqrt{7}\right)+\dfrac{371}{4}\right)-\left(\left(-35\right)\sqrt{7}+\dfrac{3}{2}+\left(\dfrac{21}{2}\right)\sqrt{7}+\left(-\dfrac{141}{2}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{23}{2}\right)\sqrt{7}\right)-\left(\left(-\dfrac{50}{7}\right)\sqrt{7}\right)\right)\right)\\ &=&\left(\left(-\dfrac{28}{5}\right)\sqrt{7}\right)-\left(\left(10\right)\sqrt{7}+\left(\dfrac{159}{2}\right)\sqrt{7}+\left(\dfrac{153}{4}\right)\sqrt{7}+\left(\dfrac{80}{9}\right)\sqrt{7}\right)+\left(\dfrac{98}{3}+\left(\dfrac{21}{2}\right)\sqrt{7}+\left(5\right)\sqrt{7}+\dfrac{308}{3}\right)-\left(\left(\left(\dfrac{9}{2}\right)\sqrt{7}\right)+\dfrac{371}{4}\right)-\left(\left(-35\right)\sqrt{7}+\dfrac{3}{2}+\left(\dfrac{21}{2}\right)\sqrt{7}+\left(-\dfrac{141}{2}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{23}{2}\right)\sqrt{7}\right)-\left(\left(-\dfrac{50}{7}\right)\sqrt{7}\right)\right)\\ &=&\left(-\dfrac{40171}{1260}\right)\sqrt{7}+\dfrac{493}{12}\\ \end{eqnarray*} \begin{eqnarray*} X-Y &=&\left(\left(\left(-\dfrac{14}{5}\right)\sqrt{28}\right)-\left(\left(2\right)\sqrt{175}+\left(\dfrac{53}{2}\right)\sqrt{63}+\left(\dfrac{51}{4}\right)\sqrt{63}+\left(\dfrac{40}{9}\right)\sqrt{28}\right)\right)-\left(\left(\left(\dfrac{14}{3}\right)\sqrt{49}+\left(\dfrac{7}{2}\right)\sqrt{63}+\left(1\right)\sqrt{175}+\left(\dfrac{44}{3}\right)\sqrt{49}\right)-\left(\left(\left(\dfrac{9}{4}\right)\sqrt{28}\right)-\left(\left(-\dfrac{53}{4}\right)\sqrt{49}\right)\right)-\left(\left(-7\right)\sqrt{175}+\dfrac{3}{2}+\left(\dfrac{7}{2}\right)\sqrt{63}+\left(-\dfrac{47}{2}\right)\sqrt{63}\right)-\left(\left(\left(-\dfrac{23}{4}\right)\sqrt{28}\right)-\left(\left(-\dfrac{10}{7}\right)\sqrt{175}\right)\right)\right)\\ &=&\left(\left(\left(-\dfrac{28}{5}\right)\sqrt{7}\right)-\left(\left(10\right)\sqrt{7}+\left(\dfrac{159}{2}\right)\sqrt{7}+\left(\dfrac{153}{4}\right)\sqrt{7}+\left(\dfrac{80}{9}\right)\sqrt{7}\right)\right)-\left(\left(\dfrac{98}{3}+\left(\dfrac{21}{2}\right)\sqrt{7}+\left(5\right)\sqrt{7}+\dfrac{308}{3}\right)-\left(\left(\left(\dfrac{9}{2}\right)\sqrt{7}\right)+\dfrac{371}{4}\right)-\left(\left(-35\right)\sqrt{7}+\dfrac{3}{2}+\left(\dfrac{21}{2}\right)\sqrt{7}+\left(-\dfrac{141}{2}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{23}{2}\right)\sqrt{7}\right)-\left(\left(-\dfrac{50}{7}\right)\sqrt{7}\right)\right)\right)\\ &=&\left(\left(-\dfrac{25603}{180}\right)\sqrt{7}\right)-\left(\dfrac{493}{12}+\left(\dfrac{1545}{14}\right)\sqrt{7}\right)\\ &=&\left(-\dfrac{25603}{180}\right)\sqrt{7}+-\dfrac{493}{12}+\left(-\dfrac{1545}{14}\right)\sqrt{7}\\ &=&\left(-\dfrac{318271}{1260}\right)\sqrt{7}-\dfrac{493}{12}\\ \end{eqnarray*} \begin{eqnarray*} X\times Y &=&\left(\left(\left(-\dfrac{14}{5}\right)\sqrt{28}\right)-\left(\left(2\right)\sqrt{175}+\left(\dfrac{53}{2}\right)\sqrt{63}+\left(\dfrac{51}{4}\right)\sqrt{63}+\left(\dfrac{40}{9}\right)\sqrt{28}\right)\right)\times\left(\left(\left(\dfrac{14}{3}\right)\sqrt{49}+\left(\dfrac{7}{2}\right)\sqrt{63}+\left(1\right)\sqrt{175}+\left(\dfrac{44}{3}\right)\sqrt{49}\right)-\left(\left(\left(\dfrac{9}{4}\right)\sqrt{28}\right)-\left(\left(-\dfrac{53}{4}\right)\sqrt{49}\right)\right)-\left(\left(-7\right)\sqrt{175}+\dfrac{3}{2}+\left(\dfrac{7}{2}\right)\sqrt{63}+\left(-\dfrac{47}{2}\right)\sqrt{63}\right)-\left(\left(\left(-\dfrac{23}{4}\right)\sqrt{28}\right)-\left(\left(-\dfrac{10}{7}\right)\sqrt{175}\right)\right)\right)\\ &=&\left(\left(\left(-\dfrac{28}{5}\right)\sqrt{7}\right)-\left(\left(10\right)\sqrt{7}+\left(\dfrac{159}{2}\right)\sqrt{7}+\left(\dfrac{153}{4}\right)\sqrt{7}+\left(\dfrac{80}{9}\right)\sqrt{7}\right)\right)\times\left(\left(\dfrac{98}{3}+\left(\dfrac{21}{2}\right)\sqrt{7}+\left(5\right)\sqrt{7}+\dfrac{308}{3}\right)-\left(\left(\left(\dfrac{9}{2}\right)\sqrt{7}\right)+\dfrac{371}{4}\right)-\left(\left(-35\right)\sqrt{7}+\dfrac{3}{2}+\left(\dfrac{21}{2}\right)\sqrt{7}+\left(-\dfrac{141}{2}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{23}{2}\right)\sqrt{7}\right)-\left(\left(-\dfrac{50}{7}\right)\sqrt{7}\right)\right)\right)\\ &=&\left(\left(-\dfrac{25603}{180}\right)\sqrt{7}\right)\left(\dfrac{493}{12}+\left(\dfrac{1545}{14}\right)\sqrt{7}\right)\\ &=&\left(-\dfrac{12622279}{2160}\right)\sqrt{7}+\left(-\dfrac{2637109}{168}\right)\sqrt{49}\\ &=&\left(-\dfrac{12622279}{2160}\right)\sqrt{7}-\dfrac{2637109}{24}\\ \end{eqnarray*}