L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(-\dfrac{41}{2}+\left(-\dfrac{43}{3}\right)\sqrt{8}+\dfrac{44}{5}\right)-\left(\left(\dfrac{63}{8}\right)\sqrt{50}\right)-\left(\left(\left(7\right)\sqrt{18}\right)-\dfrac{65}{2}\right)\) et \( Y=\left(-\dfrac{33}{7}\right)\sqrt{4}\) . 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{41}{2}+\left(-\dfrac{43}{3}\right)\sqrt{8}+\dfrac{44}{5}\right)-\left(\left(\dfrac{63}{8}\right)\sqrt{50}\right)-\left(\left(\left(7\right)\sqrt{18}\right)-\dfrac{65}{2}\right)\right)+\left(\left(-\dfrac{33}{7}\right)\sqrt{4}\right)\\
&=&\left(\left(-\dfrac{41}{2}+\left(-\dfrac{86}{3}\right)\sqrt{2}+\dfrac{44}{5}\right)-\left(\left(\dfrac{315}{8}\right)\sqrt{2}\right)-\left(\left(\left(21\right)\sqrt{2}\right)-\dfrac{65}{2}\right)\right)+\left(-\dfrac{66}{7}\right)\\
&=&\left(-\dfrac{41}{2}+\left(-\dfrac{86}{3}\right)\sqrt{2}+\dfrac{44}{5}\right)-\left(\left(\dfrac{315}{8}\right)\sqrt{2}\right)-\left(\left(\left(21\right)\sqrt{2}\right)-\dfrac{65}{2}\right)-\dfrac{66}{7}\\
&=&\dfrac{398}{35}+\left(-\dfrac{2137}{24}\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{41}{2}+\left(-\dfrac{43}{3}\right)\sqrt{8}+\dfrac{44}{5}\right)-\left(\left(\dfrac{63}{8}\right)\sqrt{50}\right)-\left(\left(\left(7\right)\sqrt{18}\right)-\dfrac{65}{2}\right)\right)-\left(\left(-\dfrac{33}{7}\right)\sqrt{4}\right)\\
&=&\left(\left(-\dfrac{41}{2}+\left(-\dfrac{86}{3}\right)\sqrt{2}+\dfrac{44}{5}\right)-\left(\left(\dfrac{315}{8}\right)\sqrt{2}\right)-\left(\left(\left(21\right)\sqrt{2}\right)-\dfrac{65}{2}\right)\right)-\left(-\dfrac{66}{7}\right)\\
&=&\left(\dfrac{104}{5}+\left(-\dfrac{2137}{24}\right)\sqrt{2}\right)-\left(-\dfrac{66}{7}\right)\\
&=&\dfrac{104}{5}+\left(-\dfrac{2137}{24}\right)\sqrt{2}+\dfrac{66}{7}\\
&=&\dfrac{1058}{35}+\left(-\dfrac{2137}{24}\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{41}{2}+\left(-\dfrac{43}{3}\right)\sqrt{8}+\dfrac{44}{5}\right)-\left(\left(\dfrac{63}{8}\right)\sqrt{50}\right)-\left(\left(\left(7\right)\sqrt{18}\right)-\dfrac{65}{2}\right)\right)\times\left(\left(-\dfrac{33}{7}\right)\sqrt{4}\right)\\
&=&\left(\left(-\dfrac{41}{2}+\left(-\dfrac{86}{3}\right)\sqrt{2}+\dfrac{44}{5}\right)-\left(\left(\dfrac{315}{8}\right)\sqrt{2}\right)-\left(\left(\left(21\right)\sqrt{2}\right)-\dfrac{65}{2}\right)\right)\times\left(-\dfrac{66}{7}\right)\\
&=&\left(\dfrac{104}{5}+\left(-\dfrac{2137}{24}\right)\sqrt{2}\right)\left(-\dfrac{66}{7}\right)\\
&=&-\dfrac{6864}{35}+\left(\dfrac{23507}{28}\right)\sqrt{2}\\
&=&-\dfrac{6864}{35}+\left(\dfrac{23507}{28}\right)\sqrt{2}\\
\end{eqnarray*}