L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(-\dfrac{80}{3}\right)\sqrt{8}+\left(\left(-\dfrac{79}{4}\right)\sqrt{8}\right)-\left(\left(\dfrac{38}{3}\right)\sqrt{50}\right)-\left(\left(\dfrac{81}{2}\right)\sqrt{8}\right)+\left(\dfrac{78}{5}\right)\sqrt{18}+\left(-5\right)\sqrt{50}\) et \( Y=\left(0\right)\sqrt{4}\) . 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{80}{3}\right)\sqrt{8}+\left(\left(-\dfrac{79}{4}\right)\sqrt{8}\right)-\left(\left(\dfrac{38}{3}\right)\sqrt{50}\right)-\left(\left(\dfrac{81}{2}\right)\sqrt{8}\right)+\left(\dfrac{78}{5}\right)\sqrt{18}+\left(-5\right)\sqrt{50}\right)+\left(\left(0\right)\sqrt{4}\right)\\
&=&\left(\left(-\dfrac{160}{3}\right)\sqrt{2}+\left(\left(-\dfrac{79}{2}\right)\sqrt{2}\right)-\left(\left(\dfrac{190}{3}\right)\sqrt{2}\right)-\left(\left(81\right)\sqrt{2}\right)+\left(\dfrac{234}{5}\right)\sqrt{2}+\left(-25\right)\sqrt{2}\right)+\left(0\right)\\
&=&\left(-\dfrac{160}{3}\right)\sqrt{2}+\left(\left(-\dfrac{79}{2}\right)\sqrt{2}\right)-\left(\left(\dfrac{190}{3}\right)\sqrt{2}\right)-\left(\left(81\right)\sqrt{2}\right)+\left(\dfrac{234}{5}\right)\sqrt{2}+\left(-25\right)\sqrt{2}+0\\
&=&\left(-\dfrac{6461}{30}\right)\sqrt{2}+0\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{80}{3}\right)\sqrt{8}+\left(\left(-\dfrac{79}{4}\right)\sqrt{8}\right)-\left(\left(\dfrac{38}{3}\right)\sqrt{50}\right)-\left(\left(\dfrac{81}{2}\right)\sqrt{8}\right)+\left(\dfrac{78}{5}\right)\sqrt{18}+\left(-5\right)\sqrt{50}\right)-\left(\left(0\right)\sqrt{4}\right)\\
&=&\left(\left(-\dfrac{160}{3}\right)\sqrt{2}+\left(\left(-\dfrac{79}{2}\right)\sqrt{2}\right)-\left(\left(\dfrac{190}{3}\right)\sqrt{2}\right)-\left(\left(81\right)\sqrt{2}\right)+\left(\dfrac{234}{5}\right)\sqrt{2}+\left(-25\right)\sqrt{2}\right)-\left(0\right)\\
&=&\left(\left(-\dfrac{6461}{30}\right)\sqrt{2}\right)-\left(0\right)\\
&=&\left(-\dfrac{6461}{30}\right)\sqrt{2}+0\\
&=&\left(-\dfrac{6461}{30}\right)\sqrt{2}+0\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{80}{3}\right)\sqrt{8}+\left(\left(-\dfrac{79}{4}\right)\sqrt{8}\right)-\left(\left(\dfrac{38}{3}\right)\sqrt{50}\right)-\left(\left(\dfrac{81}{2}\right)\sqrt{8}\right)+\left(\dfrac{78}{5}\right)\sqrt{18}+\left(-5\right)\sqrt{50}\right)\times\left(\left(0\right)\sqrt{4}\right)\\
&=&\left(\left(-\dfrac{160}{3}\right)\sqrt{2}+\left(\left(-\dfrac{79}{2}\right)\sqrt{2}\right)-\left(\left(\dfrac{190}{3}\right)\sqrt{2}\right)-\left(\left(81\right)\sqrt{2}\right)+\left(\dfrac{234}{5}\right)\sqrt{2}+\left(-25\right)\sqrt{2}\right)\times\left(0\right)\\
&=&\left(\left(-\dfrac{6461}{30}\right)\sqrt{2}\right)\left(0\right)\\
&=&\left(0\right)\sqrt{2}\\
&=&\left(0\right)\sqrt{2}\\
\end{eqnarray*}