L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Soit \( X=\left(\dfrac{15}{2}\right)\sqrt{8}\) et \( Y=\left(\left(\left(-2\right)\sqrt{4}\right)-\left(\left(6\right)\sqrt{8}\right)-\dfrac{18}{5}-\left(\left(8\right)\sqrt{18}\right)\right)-\left(\dfrac{18}{5}+\dfrac{16}{3}\right)-\left(\left(\left(-5\right)\sqrt{8}\right)-\left(\left(-\dfrac{59}{7}\right)\sqrt{8}\right)-\left(\left(-\dfrac{77}{8}\right)\sqrt{50}\right)-\dfrac{51}{2}-\left(\left(-\dfrac{13}{3}\right)\sqrt{18}\right)\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(\dfrac{15}{2}\right)\sqrt{8}\right)+\left(\left(\left(\left(-2\right)\sqrt{4}\right)-\left(\left(6\right)\sqrt{8}\right)-\dfrac{18}{5}-\left(\left(8\right)\sqrt{18}\right)\right)-\left(\dfrac{18}{5}+\dfrac{16}{3}\right)-\left(\left(\left(-5\right)\sqrt{8}\right)-\left(\left(-\dfrac{59}{7}\right)\sqrt{8}\right)-\left(\left(-\dfrac{77}{8}\right)\sqrt{50}\right)-\dfrac{51}{2}-\left(\left(-\dfrac{13}{3}\right)\sqrt{18}\right)\right)\right)\\
&=&\left(\left(15\right)\sqrt{2}\right)+\left(\left(-4-\left(\left(12\right)\sqrt{2}\right)-\dfrac{18}{5}-\left(\left(24\right)\sqrt{2}\right)\right)-\left(\dfrac{18}{5}+\dfrac{16}{3}\right)-\left(\left(\left(-10\right)\sqrt{2}\right)-\left(\left(-\dfrac{118}{7}\right)\sqrt{2}\right)-\left(\left(-\dfrac{385}{8}\right)\sqrt{2}\right)-\dfrac{51}{2}-\left(\left(-13\right)\sqrt{2}\right)\right)\right)\\
&=&\left(15\right)\sqrt{2}+\left(-4-\left(\left(12\right)\sqrt{2}\right)-\dfrac{18}{5}-\left(\left(24\right)\sqrt{2}\right)\right)-\left(\dfrac{18}{5}+\dfrac{16}{3}\right)-\left(\left(\left(-10\right)\sqrt{2}\right)-\left(\left(-\dfrac{118}{7}\right)\sqrt{2}\right)-\left(\left(-\dfrac{385}{8}\right)\sqrt{2}\right)-\dfrac{51}{2}-\left(\left(-13\right)\sqrt{2}\right)\right)\\
&=&\left(-\dfrac{4983}{56}\right)\sqrt{2}+\dfrac{269}{30}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\dfrac{15}{2}\right)\sqrt{8}\right)-\left(\left(\left(\left(-2\right)\sqrt{4}\right)-\left(\left(6\right)\sqrt{8}\right)-\dfrac{18}{5}-\left(\left(8\right)\sqrt{18}\right)\right)-\left(\dfrac{18}{5}+\dfrac{16}{3}\right)-\left(\left(\left(-5\right)\sqrt{8}\right)-\left(\left(-\dfrac{59}{7}\right)\sqrt{8}\right)-\left(\left(-\dfrac{77}{8}\right)\sqrt{50}\right)-\dfrac{51}{2}-\left(\left(-\dfrac{13}{3}\right)\sqrt{18}\right)\right)\right)\\
&=&\left(\left(15\right)\sqrt{2}\right)-\left(\left(-4-\left(\left(12\right)\sqrt{2}\right)-\dfrac{18}{5}-\left(\left(24\right)\sqrt{2}\right)\right)-\left(\dfrac{18}{5}+\dfrac{16}{3}\right)-\left(\left(\left(-10\right)\sqrt{2}\right)-\left(\left(-\dfrac{118}{7}\right)\sqrt{2}\right)-\left(\left(-\dfrac{385}{8}\right)\sqrt{2}\right)-\dfrac{51}{2}-\left(\left(-13\right)\sqrt{2}\right)\right)\right)\\
&=&\left(\left(15\right)\sqrt{2}\right)-\left(\dfrac{269}{30}+\left(-\dfrac{5823}{56}\right)\sqrt{2}\right)\\
&=&\left(15\right)\sqrt{2}+-\dfrac{269}{30}+\left(\dfrac{5823}{56}\right)\sqrt{2}\\
&=&\left(\dfrac{6663}{56}\right)\sqrt{2}-\dfrac{269}{30}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\dfrac{15}{2}\right)\sqrt{8}\right)\times\left(\left(\left(\left(-2\right)\sqrt{4}\right)-\left(\left(6\right)\sqrt{8}\right)-\dfrac{18}{5}-\left(\left(8\right)\sqrt{18}\right)\right)-\left(\dfrac{18}{5}+\dfrac{16}{3}\right)-\left(\left(\left(-5\right)\sqrt{8}\right)-\left(\left(-\dfrac{59}{7}\right)\sqrt{8}\right)-\left(\left(-\dfrac{77}{8}\right)\sqrt{50}\right)-\dfrac{51}{2}-\left(\left(-\dfrac{13}{3}\right)\sqrt{18}\right)\right)\right)\\
&=&\left(\left(15\right)\sqrt{2}\right)\times\left(\left(-4-\left(\left(12\right)\sqrt{2}\right)-\dfrac{18}{5}-\left(\left(24\right)\sqrt{2}\right)\right)-\left(\dfrac{18}{5}+\dfrac{16}{3}\right)-\left(\left(\left(-10\right)\sqrt{2}\right)-\left(\left(-\dfrac{118}{7}\right)\sqrt{2}\right)-\left(\left(-\dfrac{385}{8}\right)\sqrt{2}\right)-\dfrac{51}{2}-\left(\left(-13\right)\sqrt{2}\right)\right)\right)\\
&=&\left(\left(15\right)\sqrt{2}\right)\left(\dfrac{269}{30}+\left(-\dfrac{5823}{56}\right)\sqrt{2}\right)\\
&=&\left(\dfrac{269}{2}\right)\sqrt{2}+\left(-\dfrac{87345}{56}\right)\sqrt{4}\\
&=&\left(\dfrac{269}{2}\right)\sqrt{2}-\dfrac{87345}{28}\\
\end{eqnarray*}