L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(-\dfrac{59}{6}\right)\sqrt{18}\) et \( Y=\left(\left(-\dfrac{19}{2}\right)\sqrt{4}\right)-\left(\left(\left(-\dfrac{55}{7}\right)\sqrt{4}\right)-\left(\left(-\dfrac{14}{5}\right)\sqrt{8}\right)\right)-\left(\left(\dfrac{3}{2}\right)\sqrt{50}\right)\) . 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{59}{6}\right)\sqrt{18}\right)+\left(\left(\left(-\dfrac{19}{2}\right)\sqrt{4}\right)-\left(\left(\left(-\dfrac{55}{7}\right)\sqrt{4}\right)-\left(\left(-\dfrac{14}{5}\right)\sqrt{8}\right)\right)-\left(\left(\dfrac{3}{2}\right)\sqrt{50}\right)\right)\\
&=&\left(\left(-\dfrac{59}{2}\right)\sqrt{2}\right)+\left(-19-\left(-\dfrac{110}{7}-\left(\left(-\dfrac{28}{5}\right)\sqrt{2}\right)\right)-\left(\left(\dfrac{15}{2}\right)\sqrt{2}\right)\right)\\
&=&\left(-\dfrac{59}{2}\right)\sqrt{2}-19-\left(-\dfrac{110}{7}-\left(\left(-\dfrac{28}{5}\right)\sqrt{2}\right)\right)-\left(\left(\dfrac{15}{2}\right)\sqrt{2}\right)\\
&=&\left(-\dfrac{213}{5}\right)\sqrt{2}-\dfrac{23}{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{59}{6}\right)\sqrt{18}\right)-\left(\left(\left(-\dfrac{19}{2}\right)\sqrt{4}\right)-\left(\left(\left(-\dfrac{55}{7}\right)\sqrt{4}\right)-\left(\left(-\dfrac{14}{5}\right)\sqrt{8}\right)\right)-\left(\left(\dfrac{3}{2}\right)\sqrt{50}\right)\right)\\
&=&\left(\left(-\dfrac{59}{2}\right)\sqrt{2}\right)-\left(-19-\left(-\dfrac{110}{7}-\left(\left(-\dfrac{28}{5}\right)\sqrt{2}\right)\right)-\left(\left(\dfrac{15}{2}\right)\sqrt{2}\right)\right)\\
&=&\left(\left(-\dfrac{59}{2}\right)\sqrt{2}\right)-\left(-\dfrac{23}{7}+\left(-\dfrac{131}{10}\right)\sqrt{2}\right)\\
&=&\left(-\dfrac{59}{2}\right)\sqrt{2}+\dfrac{23}{7}+\left(\dfrac{131}{10}\right)\sqrt{2}\\
&=&\left(-\dfrac{82}{5}\right)\sqrt{2}+\dfrac{23}{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{59}{6}\right)\sqrt{18}\right)\times\left(\left(\left(-\dfrac{19}{2}\right)\sqrt{4}\right)-\left(\left(\left(-\dfrac{55}{7}\right)\sqrt{4}\right)-\left(\left(-\dfrac{14}{5}\right)\sqrt{8}\right)\right)-\left(\left(\dfrac{3}{2}\right)\sqrt{50}\right)\right)\\
&=&\left(\left(-\dfrac{59}{2}\right)\sqrt{2}\right)\times\left(-19-\left(-\dfrac{110}{7}-\left(\left(-\dfrac{28}{5}\right)\sqrt{2}\right)\right)-\left(\left(\dfrac{15}{2}\right)\sqrt{2}\right)\right)\\
&=&\left(\left(-\dfrac{59}{2}\right)\sqrt{2}\right)\left(-\dfrac{23}{7}+\left(-\dfrac{131}{10}\right)\sqrt{2}\right)\\
&=&\left(\dfrac{1357}{14}\right)\sqrt{2}+\left(\dfrac{7729}{20}\right)\sqrt{4}\\
&=&\left(\dfrac{1357}{14}\right)\sqrt{2}+\dfrac{7729}{10}\\
\end{eqnarray*}