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{63}{2}\right)\sqrt{63}+\left(\dfrac{23}{2}\right)\sqrt{175}+\left(\dfrac{31}{3}\right)\sqrt{175}+\left(\dfrac{2}{9}\right)\sqrt{175}\right)-\left(\left(\left(\dfrac{2}{3}\right)\sqrt{175}\right)-\left(\left(-\dfrac{5}{3}\right)\sqrt{49}\right)-\left(\left(0\right)\sqrt{28}\right)-\left(\left(-\dfrac{43}{9}\right)\sqrt{63}\right)-\left(\left(\dfrac{3}{2}\right)\sqrt{28}\right)\right)-\left(\left(\dfrac{31}{2}\right)\sqrt{175}\right)-\left(\left(\left(-\dfrac{44}{9}\right)\sqrt{63}\right)+\dfrac{17}{2}\right)-\left(\left(\dfrac{21}{2}\right)\sqrt{28}\right)$ et $ Y=-9+\dfrac{23}{9}+\left(\dfrac{73}{2}\right)\sqrt{28}-1+\left(-\dfrac{22}{7}\right)\sqrt{175}+\left(\left(-\dfrac{14}{3}\right)\sqrt{49}\right)-\left(\left(\dfrac{9}{2}\right)\sqrt{63}\right)-\left(\left(3\right)\sqrt{63}\right)-\dfrac{39}{4}-\left(\left(-\dfrac{16}{3}\right)\sqrt{63}\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{63}{2}\right)\sqrt{63}+\left(\dfrac{23}{2}\right)\sqrt{175}+\left(\dfrac{31}{3}\right)\sqrt{175}+\left(\dfrac{2}{9}\right)\sqrt{175}\right)-\left(\left(\left(\dfrac{2}{3}\right)\sqrt{175}\right)-\left(\left(-\dfrac{5}{3}\right)\sqrt{49}\right)-\left(\left(0\right)\sqrt{28}\right)-\left(\left(-\dfrac{43}{9}\right)\sqrt{63}\right)-\left(\left(\dfrac{3}{2}\right)\sqrt{28}\right)\right)-\left(\left(\dfrac{31}{2}\right)\sqrt{175}\right)-\left(\left(\left(-\dfrac{44}{9}\right)\sqrt{63}\right)+\dfrac{17}{2}\right)-\left(\left(\dfrac{21}{2}\right)\sqrt{28}\right)\right)+\left(-9+\dfrac{23}{9}+\left(\dfrac{73}{2}\right)\sqrt{28}-1+\left(-\dfrac{22}{7}\right)\sqrt{175}+\left(\left(-\dfrac{14}{3}\right)\sqrt{49}\right)-\left(\left(\dfrac{9}{2}\right)\sqrt{63}\right)-\left(\left(3\right)\sqrt{63}\right)-\dfrac{39}{4}-\left(\left(-\dfrac{16}{3}\right)\sqrt{63}\right)\right)\\ &=&\left(\left(\left(-\dfrac{189}{2}\right)\sqrt{7}+\left(\dfrac{115}{2}\right)\sqrt{7}+\left(\dfrac{155}{3}\right)\sqrt{7}+\left(\dfrac{10}{9}\right)\sqrt{7}\right)-\left(\left(\left(\dfrac{10}{3}\right)\sqrt{7}\right)+\dfrac{35}{3}-\left(\left(0\right)\sqrt{7}\right)-\left(\left(-\dfrac{43}{3}\right)\sqrt{7}\right)-\left(\left(3\right)\sqrt{7}\right)\right)-\left(\left(\dfrac{155}{2}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{44}{3}\right)\sqrt{7}\right)+\dfrac{17}{2}\right)-\left(\left(21\right)\sqrt{7}\right)\right)+\left(-9+\dfrac{23}{9}+\left(73\right)\sqrt{7}-1+\left(-\dfrac{110}{7}\right)\sqrt{7}-\dfrac{98}{3}-\left(\left(\dfrac{27}{2}\right)\sqrt{7}\right)-\left(\left(9\right)\sqrt{7}\right)-\dfrac{39}{4}-\left(\left(-16\right)\sqrt{7}\right)\right)\\ &=&\left(\left(-\dfrac{189}{2}\right)\sqrt{7}+\left(\dfrac{115}{2}\right)\sqrt{7}+\left(\dfrac{155}{3}\right)\sqrt{7}+\left(\dfrac{10}{9}\right)\sqrt{7}\right)-\left(\left(\left(\dfrac{10}{3}\right)\sqrt{7}\right)+\dfrac{35}{3}-\left(\left(0\right)\sqrt{7}\right)-\left(\left(-\dfrac{43}{3}\right)\sqrt{7}\right)-\left(\left(3\right)\sqrt{7}\right)\right)-\left(\left(\dfrac{155}{2}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{44}{3}\right)\sqrt{7}\right)+\dfrac{17}{2}\right)-\left(\left(21\right)\sqrt{7}\right)-9+\dfrac{23}{9}+\left(73\right)\sqrt{7}-1+\left(-\dfrac{110}{7}\right)\sqrt{7}-\dfrac{98}{3}-\left(\left(\dfrac{27}{2}\right)\sqrt{7}\right)-\left(\left(9\right)\sqrt{7}\right)-\dfrac{39}{4}-\left(\left(-16\right)\sqrt{7}\right)\\ &=&\left(-\dfrac{2012}{63}\right)\sqrt{7}-\dfrac{2521}{36}\\ \end{eqnarray*} \begin{eqnarray*} X-Y &=&\left(\left(\left(-\dfrac{63}{2}\right)\sqrt{63}+\left(\dfrac{23}{2}\right)\sqrt{175}+\left(\dfrac{31}{3}\right)\sqrt{175}+\left(\dfrac{2}{9}\right)\sqrt{175}\right)-\left(\left(\left(\dfrac{2}{3}\right)\sqrt{175}\right)-\left(\left(-\dfrac{5}{3}\right)\sqrt{49}\right)-\left(\left(0\right)\sqrt{28}\right)-\left(\left(-\dfrac{43}{9}\right)\sqrt{63}\right)-\left(\left(\dfrac{3}{2}\right)\sqrt{28}\right)\right)-\left(\left(\dfrac{31}{2}\right)\sqrt{175}\right)-\left(\left(\left(-\dfrac{44}{9}\right)\sqrt{63}\right)+\dfrac{17}{2}\right)-\left(\left(\dfrac{21}{2}\right)\sqrt{28}\right)\right)-\left(-9+\dfrac{23}{9}+\left(\dfrac{73}{2}\right)\sqrt{28}-1+\left(-\dfrac{22}{7}\right)\sqrt{175}+\left(\left(-\dfrac{14}{3}\right)\sqrt{49}\right)-\left(\left(\dfrac{9}{2}\right)\sqrt{63}\right)-\left(\left(3\right)\sqrt{63}\right)-\dfrac{39}{4}-\left(\left(-\dfrac{16}{3}\right)\sqrt{63}\right)\right)\\ &=&\left(\left(\left(-\dfrac{189}{2}\right)\sqrt{7}+\left(\dfrac{115}{2}\right)\sqrt{7}+\left(\dfrac{155}{3}\right)\sqrt{7}+\left(\dfrac{10}{9}\right)\sqrt{7}\right)-\left(\left(\left(\dfrac{10}{3}\right)\sqrt{7}\right)+\dfrac{35}{3}-\left(\left(0\right)\sqrt{7}\right)-\left(\left(-\dfrac{43}{3}\right)\sqrt{7}\right)-\left(\left(3\right)\sqrt{7}\right)\right)-\left(\left(\dfrac{155}{2}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{44}{3}\right)\sqrt{7}\right)+\dfrac{17}{2}\right)-\left(\left(21\right)\sqrt{7}\right)\right)-\left(-9+\dfrac{23}{9}+\left(73\right)\sqrt{7}-1+\left(-\dfrac{110}{7}\right)\sqrt{7}-\dfrac{98}{3}-\left(\left(\dfrac{27}{2}\right)\sqrt{7}\right)-\left(\left(9\right)\sqrt{7}\right)-\dfrac{39}{4}-\left(\left(-16\right)\sqrt{7}\right)\right)\\ &=&\left(\left(-\dfrac{1489}{18}\right)\sqrt{7}-\dfrac{121}{6}\right)-\left(-\dfrac{1795}{36}+\left(\dfrac{711}{14}\right)\sqrt{7}\right)\\ &=&\left(-\dfrac{1489}{18}\right)\sqrt{7}-\dfrac{121}{6}+\dfrac{1795}{36}+\left(-\dfrac{711}{14}\right)\sqrt{7}\\ &=&\left(-\dfrac{8411}{63}\right)\sqrt{7}+\dfrac{1069}{36}\\ \end{eqnarray*} \begin{eqnarray*} X\times Y &=&\left(\left(\left(-\dfrac{63}{2}\right)\sqrt{63}+\left(\dfrac{23}{2}\right)\sqrt{175}+\left(\dfrac{31}{3}\right)\sqrt{175}+\left(\dfrac{2}{9}\right)\sqrt{175}\right)-\left(\left(\left(\dfrac{2}{3}\right)\sqrt{175}\right)-\left(\left(-\dfrac{5}{3}\right)\sqrt{49}\right)-\left(\left(0\right)\sqrt{28}\right)-\left(\left(-\dfrac{43}{9}\right)\sqrt{63}\right)-\left(\left(\dfrac{3}{2}\right)\sqrt{28}\right)\right)-\left(\left(\dfrac{31}{2}\right)\sqrt{175}\right)-\left(\left(\left(-\dfrac{44}{9}\right)\sqrt{63}\right)+\dfrac{17}{2}\right)-\left(\left(\dfrac{21}{2}\right)\sqrt{28}\right)\right)\times\left(-9+\dfrac{23}{9}+\left(\dfrac{73}{2}\right)\sqrt{28}-1+\left(-\dfrac{22}{7}\right)\sqrt{175}+\left(\left(-\dfrac{14}{3}\right)\sqrt{49}\right)-\left(\left(\dfrac{9}{2}\right)\sqrt{63}\right)-\left(\left(3\right)\sqrt{63}\right)-\dfrac{39}{4}-\left(\left(-\dfrac{16}{3}\right)\sqrt{63}\right)\right)\\ &=&\left(\left(\left(-\dfrac{189}{2}\right)\sqrt{7}+\left(\dfrac{115}{2}\right)\sqrt{7}+\left(\dfrac{155}{3}\right)\sqrt{7}+\left(\dfrac{10}{9}\right)\sqrt{7}\right)-\left(\left(\left(\dfrac{10}{3}\right)\sqrt{7}\right)+\dfrac{35}{3}-\left(\left(0\right)\sqrt{7}\right)-\left(\left(-\dfrac{43}{3}\right)\sqrt{7}\right)-\left(\left(3\right)\sqrt{7}\right)\right)-\left(\left(\dfrac{155}{2}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{44}{3}\right)\sqrt{7}\right)+\dfrac{17}{2}\right)-\left(\left(21\right)\sqrt{7}\right)\right)\times\left(-9+\dfrac{23}{9}+\left(73\right)\sqrt{7}-1+\left(-\dfrac{110}{7}\right)\sqrt{7}-\dfrac{98}{3}-\left(\left(\dfrac{27}{2}\right)\sqrt{7}\right)-\left(\left(9\right)\sqrt{7}\right)-\dfrac{39}{4}-\left(\left(-16\right)\sqrt{7}\right)\right)\\ &=&\left(\left(-\dfrac{1489}{18}\right)\sqrt{7}-\dfrac{121}{6}\right)\left(-\dfrac{1795}{36}+\left(\dfrac{711}{14}\right)\sqrt{7}\right)\\ &=&\left(\dfrac{14063611}{4536}\right)\sqrt{7}+\left(-\dfrac{117631}{28}\right)\sqrt{49}+\dfrac{217195}{216}\\ &=&\left(\dfrac{14063611}{4536}\right)\sqrt{7}-\dfrac{6134879}{216}\\ \end{eqnarray*}