L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Soit \( X=\left(-3\right)\sqrt{4}\) et \( Y=\left(-8\right)\sqrt{18}+\left(-2\right)\sqrt{18}+\left(-\dfrac{29}{8}\right)\sqrt{8}+\left(5\right)\sqrt{4}+\dfrac{54}{5}+\left(\left(-\dfrac{7}{3}\right)\sqrt{8}\right)-\left(\left(-9\right)\sqrt{18}\right)-\left(\left(-\dfrac{29}{8}\right)\sqrt{8}\right)-\left(\left(5\right)\sqrt{4}\right)+\left(\left(0\right)\sqrt{8}\right)-\left(\left(\dfrac{53}{7}\right)\sqrt{50}\right)-\left(\left(\dfrac{7}{8}\right)\sqrt{18}\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(-3\right)\sqrt{4}\right)+\left(\left(-8\right)\sqrt{18}+\left(-2\right)\sqrt{18}+\left(-\dfrac{29}{8}\right)\sqrt{8}+\left(5\right)\sqrt{4}+\dfrac{54}{5}+\left(\left(-\dfrac{7}{3}\right)\sqrt{8}\right)-\left(\left(-9\right)\sqrt{18}\right)-\left(\left(-\dfrac{29}{8}\right)\sqrt{8}\right)-\left(\left(5\right)\sqrt{4}\right)+\left(\left(0\right)\sqrt{8}\right)-\left(\left(\dfrac{53}{7}\right)\sqrt{50}\right)-\left(\left(\dfrac{7}{8}\right)\sqrt{18}\right)\right)\\
&=&\left(-6\right)+\left(\left(-24\right)\sqrt{2}+\left(-6\right)\sqrt{2}+\left(-\dfrac{29}{4}\right)\sqrt{2}+10+\dfrac{54}{5}+\left(\left(-\dfrac{14}{3}\right)\sqrt{2}\right)-\left(\left(-27\right)\sqrt{2}\right)-\left(\left(-\dfrac{29}{4}\right)\sqrt{2}\right)-10+\left(\left(0\right)\sqrt{2}\right)-\left(\left(\dfrac{265}{7}\right)\sqrt{2}\right)-\left(\left(\dfrac{21}{8}\right)\sqrt{2}\right)\right)\\
&=&-6+\left(-24\right)\sqrt{2}+\left(-6\right)\sqrt{2}+\left(-\dfrac{29}{4}\right)\sqrt{2}+10+\dfrac{54}{5}+\left(\left(-\dfrac{14}{3}\right)\sqrt{2}\right)-\left(\left(-27\right)\sqrt{2}\right)-\left(\left(-\dfrac{29}{4}\right)\sqrt{2}\right)-10+\left(\left(0\right)\sqrt{2}\right)-\left(\left(\dfrac{265}{7}\right)\sqrt{2}\right)-\left(\left(\dfrac{21}{8}\right)\sqrt{2}\right)\\
&=&\dfrac{24}{5}+\left(-\dfrac{8089}{168}\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-3\right)\sqrt{4}\right)-\left(\left(-8\right)\sqrt{18}+\left(-2\right)\sqrt{18}+\left(-\dfrac{29}{8}\right)\sqrt{8}+\left(5\right)\sqrt{4}+\dfrac{54}{5}+\left(\left(-\dfrac{7}{3}\right)\sqrt{8}\right)-\left(\left(-9\right)\sqrt{18}\right)-\left(\left(-\dfrac{29}{8}\right)\sqrt{8}\right)-\left(\left(5\right)\sqrt{4}\right)+\left(\left(0\right)\sqrt{8}\right)-\left(\left(\dfrac{53}{7}\right)\sqrt{50}\right)-\left(\left(\dfrac{7}{8}\right)\sqrt{18}\right)\right)\\
&=&\left(-6\right)-\left(\left(-24\right)\sqrt{2}+\left(-6\right)\sqrt{2}+\left(-\dfrac{29}{4}\right)\sqrt{2}+10+\dfrac{54}{5}+\left(\left(-\dfrac{14}{3}\right)\sqrt{2}\right)-\left(\left(-27\right)\sqrt{2}\right)-\left(\left(-\dfrac{29}{4}\right)\sqrt{2}\right)-10+\left(\left(0\right)\sqrt{2}\right)-\left(\left(\dfrac{265}{7}\right)\sqrt{2}\right)-\left(\left(\dfrac{21}{8}\right)\sqrt{2}\right)\right)\\
&=&\left(-6\right)-\left(\left(-\dfrac{8089}{168}\right)\sqrt{2}+\dfrac{54}{5}\right)\\
&=&-6+\left(\dfrac{8089}{168}\right)\sqrt{2}-\dfrac{54}{5}\\
&=&-\dfrac{84}{5}+\left(\dfrac{8089}{168}\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-3\right)\sqrt{4}\right)\times\left(\left(-8\right)\sqrt{18}+\left(-2\right)\sqrt{18}+\left(-\dfrac{29}{8}\right)\sqrt{8}+\left(5\right)\sqrt{4}+\dfrac{54}{5}+\left(\left(-\dfrac{7}{3}\right)\sqrt{8}\right)-\left(\left(-9\right)\sqrt{18}\right)-\left(\left(-\dfrac{29}{8}\right)\sqrt{8}\right)-\left(\left(5\right)\sqrt{4}\right)+\left(\left(0\right)\sqrt{8}\right)-\left(\left(\dfrac{53}{7}\right)\sqrt{50}\right)-\left(\left(\dfrac{7}{8}\right)\sqrt{18}\right)\right)\\
&=&\left(-6\right)\times\left(\left(-24\right)\sqrt{2}+\left(-6\right)\sqrt{2}+\left(-\dfrac{29}{4}\right)\sqrt{2}+10+\dfrac{54}{5}+\left(\left(-\dfrac{14}{3}\right)\sqrt{2}\right)-\left(\left(-27\right)\sqrt{2}\right)-\left(\left(-\dfrac{29}{4}\right)\sqrt{2}\right)-10+\left(\left(0\right)\sqrt{2}\right)-\left(\left(\dfrac{265}{7}\right)\sqrt{2}\right)-\left(\left(\dfrac{21}{8}\right)\sqrt{2}\right)\right)\\
&=&\left(-6\right)\left(\left(-\dfrac{8089}{168}\right)\sqrt{2}+\dfrac{54}{5}\right)\\
&=&\left(\dfrac{8089}{28}\right)\sqrt{2}-\dfrac{324}{5}\\
&=&\left(\dfrac{8089}{28}\right)\sqrt{2}-\dfrac{324}{5}\\
\end{eqnarray*}