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(4\right)\sqrt{49}+\left(-\dfrac{53}{5}\right)\sqrt{49}+\left(\dfrac{35}{4}\right)\sqrt{28}+\left(0\right)\sqrt{175}+\left(\dfrac{3}{8}\right)\sqrt{28}+\left(\left(\dfrac{35}{4}\right)\sqrt{28}\right)-\left(\left(-\dfrac{11}{8}\right)\sqrt{63}\right)+\left(\dfrac{67}{3}\right)\sqrt{28}$ et $ Y=\left(\dfrac{63}{4}+\left(\dfrac{77}{8}\right)\sqrt{63}+\left(-\dfrac{13}{7}\right)\sqrt{49}+\left(\dfrac{14}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{45}{4}\right)\sqrt{28}\right)-\left(\left(\dfrac{77}{8}\right)\sqrt{63}+\left(-\dfrac{13}{8}\right)\sqrt{28}+2+\left(-\dfrac{15}{7}\right)\sqrt{63}\right)-\left(\left(\left(-\dfrac{1}{6}\right)\sqrt{63}\right)-\left(\left(-2\right)\sqrt{63}\right)-\left(\left(6\right)\sqrt{63}\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(4\right)\sqrt{49}+\left(-\dfrac{53}{5}\right)\sqrt{49}+\left(\dfrac{35}{4}\right)\sqrt{28}+\left(0\right)\sqrt{175}+\left(\dfrac{3}{8}\right)\sqrt{28}+\left(\left(\dfrac{35}{4}\right)\sqrt{28}\right)-\left(\left(-\dfrac{11}{8}\right)\sqrt{63}\right)+\left(\dfrac{67}{3}\right)\sqrt{28}\right)+\left(\left(\dfrac{63}{4}+\left(\dfrac{77}{8}\right)\sqrt{63}+\left(-\dfrac{13}{7}\right)\sqrt{49}+\left(\dfrac{14}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{45}{4}\right)\sqrt{28}\right)-\left(\left(\dfrac{77}{8}\right)\sqrt{63}+\left(-\dfrac{13}{8}\right)\sqrt{28}+2+\left(-\dfrac{15}{7}\right)\sqrt{63}\right)-\left(\left(\left(-\dfrac{1}{6}\right)\sqrt{63}\right)-\left(\left(-2\right)\sqrt{63}\right)-\left(\left(6\right)\sqrt{63}\right)\right)\right)\\ &=&\left(28-\dfrac{371}{5}+\left(\dfrac{35}{2}\right)\sqrt{7}+\left(0\right)\sqrt{7}+\left(\dfrac{3}{4}\right)\sqrt{7}+\left(\left(\dfrac{35}{2}\right)\sqrt{7}\right)-\left(\left(-\dfrac{33}{8}\right)\sqrt{7}\right)+\left(\dfrac{134}{3}\right)\sqrt{7}\right)+\left(\left(\dfrac{63}{4}+\left(\dfrac{231}{8}\right)\sqrt{7}-13+\left(14\right)\sqrt{7}\right)-\left(\left(\dfrac{45}{2}\right)\sqrt{7}\right)-\left(\left(\dfrac{231}{8}\right)\sqrt{7}+\left(-\dfrac{13}{4}\right)\sqrt{7}+2+\left(-\dfrac{45}{7}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{1}{2}\right)\sqrt{7}\right)-\left(\left(-6\right)\sqrt{7}\right)-\left(\left(18\right)\sqrt{7}\right)\right)\right)\\ &=&28-\dfrac{371}{5}+\left(\dfrac{35}{2}\right)\sqrt{7}+\left(0\right)\sqrt{7}+\left(\dfrac{3}{4}\right)\sqrt{7}+\left(\left(\dfrac{35}{2}\right)\sqrt{7}\right)-\left(\left(-\dfrac{33}{8}\right)\sqrt{7}\right)+\left(\dfrac{134}{3}\right)\sqrt{7}+\left(\dfrac{63}{4}+\left(\dfrac{231}{8}\right)\sqrt{7}-13+\left(14\right)\sqrt{7}\right)-\left(\left(\dfrac{45}{2}\right)\sqrt{7}\right)-\left(\left(\dfrac{231}{8}\right)\sqrt{7}+\left(-\dfrac{13}{4}\right)\sqrt{7}+2+\left(-\dfrac{45}{7}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{1}{2}\right)\sqrt{7}\right)-\left(\left(-6\right)\sqrt{7}\right)-\left(\left(18\right)\sqrt{7}\right)\right)\\ &=&-\dfrac{909}{20}+\left(\dfrac{16501}{168}\right)\sqrt{7}\\ \end{eqnarray*} \begin{eqnarray*} X-Y &=&\left(\left(4\right)\sqrt{49}+\left(-\dfrac{53}{5}\right)\sqrt{49}+\left(\dfrac{35}{4}\right)\sqrt{28}+\left(0\right)\sqrt{175}+\left(\dfrac{3}{8}\right)\sqrt{28}+\left(\left(\dfrac{35}{4}\right)\sqrt{28}\right)-\left(\left(-\dfrac{11}{8}\right)\sqrt{63}\right)+\left(\dfrac{67}{3}\right)\sqrt{28}\right)-\left(\left(\dfrac{63}{4}+\left(\dfrac{77}{8}\right)\sqrt{63}+\left(-\dfrac{13}{7}\right)\sqrt{49}+\left(\dfrac{14}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{45}{4}\right)\sqrt{28}\right)-\left(\left(\dfrac{77}{8}\right)\sqrt{63}+\left(-\dfrac{13}{8}\right)\sqrt{28}+2+\left(-\dfrac{15}{7}\right)\sqrt{63}\right)-\left(\left(\left(-\dfrac{1}{6}\right)\sqrt{63}\right)-\left(\left(-2\right)\sqrt{63}\right)-\left(\left(6\right)\sqrt{63}\right)\right)\right)\\ &=&\left(28-\dfrac{371}{5}+\left(\dfrac{35}{2}\right)\sqrt{7}+\left(0\right)\sqrt{7}+\left(\dfrac{3}{4}\right)\sqrt{7}+\left(\left(\dfrac{35}{2}\right)\sqrt{7}\right)-\left(\left(-\dfrac{33}{8}\right)\sqrt{7}\right)+\left(\dfrac{134}{3}\right)\sqrt{7}\right)-\left(\left(\dfrac{63}{4}+\left(\dfrac{231}{8}\right)\sqrt{7}-13+\left(14\right)\sqrt{7}\right)-\left(\left(\dfrac{45}{2}\right)\sqrt{7}\right)-\left(\left(\dfrac{231}{8}\right)\sqrt{7}+\left(-\dfrac{13}{4}\right)\sqrt{7}+2+\left(-\dfrac{45}{7}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{1}{2}\right)\sqrt{7}\right)-\left(\left(-6\right)\sqrt{7}\right)-\left(\left(18\right)\sqrt{7}\right)\right)\right)\\ &=&\left(-\dfrac{231}{5}+\left(\dfrac{2029}{24}\right)\sqrt{7}\right)-\left(\dfrac{3}{4}+\left(\dfrac{383}{28}\right)\sqrt{7}\right)\\ &=&-\dfrac{231}{5}+\left(\dfrac{2029}{24}\right)\sqrt{7}+-\dfrac{3}{4}+\left(-\dfrac{383}{28}\right)\sqrt{7}\\ &=&-\dfrac{939}{20}+\left(\dfrac{11905}{168}\right)\sqrt{7}\\ \end{eqnarray*} \begin{eqnarray*} X\times Y &=&\left(\left(4\right)\sqrt{49}+\left(-\dfrac{53}{5}\right)\sqrt{49}+\left(\dfrac{35}{4}\right)\sqrt{28}+\left(0\right)\sqrt{175}+\left(\dfrac{3}{8}\right)\sqrt{28}+\left(\left(\dfrac{35}{4}\right)\sqrt{28}\right)-\left(\left(-\dfrac{11}{8}\right)\sqrt{63}\right)+\left(\dfrac{67}{3}\right)\sqrt{28}\right)\times\left(\left(\dfrac{63}{4}+\left(\dfrac{77}{8}\right)\sqrt{63}+\left(-\dfrac{13}{7}\right)\sqrt{49}+\left(\dfrac{14}{3}\right)\sqrt{63}\right)-\left(\left(\dfrac{45}{4}\right)\sqrt{28}\right)-\left(\left(\dfrac{77}{8}\right)\sqrt{63}+\left(-\dfrac{13}{8}\right)\sqrt{28}+2+\left(-\dfrac{15}{7}\right)\sqrt{63}\right)-\left(\left(\left(-\dfrac{1}{6}\right)\sqrt{63}\right)-\left(\left(-2\right)\sqrt{63}\right)-\left(\left(6\right)\sqrt{63}\right)\right)\right)\\ &=&\left(28-\dfrac{371}{5}+\left(\dfrac{35}{2}\right)\sqrt{7}+\left(0\right)\sqrt{7}+\left(\dfrac{3}{4}\right)\sqrt{7}+\left(\left(\dfrac{35}{2}\right)\sqrt{7}\right)-\left(\left(-\dfrac{33}{8}\right)\sqrt{7}\right)+\left(\dfrac{134}{3}\right)\sqrt{7}\right)\times\left(\left(\dfrac{63}{4}+\left(\dfrac{231}{8}\right)\sqrt{7}-13+\left(14\right)\sqrt{7}\right)-\left(\left(\dfrac{45}{2}\right)\sqrt{7}\right)-\left(\left(\dfrac{231}{8}\right)\sqrt{7}+\left(-\dfrac{13}{4}\right)\sqrt{7}+2+\left(-\dfrac{45}{7}\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{1}{2}\right)\sqrt{7}\right)-\left(\left(-6\right)\sqrt{7}\right)-\left(\left(18\right)\sqrt{7}\right)\right)\right)\\ &=&\left(-\dfrac{231}{5}+\left(\dfrac{2029}{24}\right)\sqrt{7}\right)\left(\dfrac{3}{4}+\left(\dfrac{383}{28}\right)\sqrt{7}\right)\\ &=&-\dfrac{693}{20}+\left(-\dfrac{90967}{160}\right)\sqrt{7}+\left(\dfrac{777107}{672}\right)\sqrt{49}\\ &=&\dfrac{3868903}{480}+\left(-\dfrac{90967}{160}\right)\sqrt{7}\\ \end{eqnarray*}