L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(\dfrac{21}{2}\right)\sqrt{18}+\left(-\dfrac{6}{5}\right)\sqrt{50}+\left(\dfrac{39}{2}\right)\sqrt{50}+\left(\left(\dfrac{39}{2}\right)\sqrt{50}\right)-\left(\left(-\dfrac{3}{2}\right)\sqrt{4}\right)-\left(\left(-\dfrac{49}{6}\right)\sqrt{8}\right)+\left(-\dfrac{49}{6}\right)\sqrt{8}\) et \( Y=4\) . 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{21}{2}\right)\sqrt{18}+\left(-\dfrac{6}{5}\right)\sqrt{50}+\left(\dfrac{39}{2}\right)\sqrt{50}+\left(\left(\dfrac{39}{2}\right)\sqrt{50}\right)-\left(\left(-\dfrac{3}{2}\right)\sqrt{4}\right)-\left(\left(-\dfrac{49}{6}\right)\sqrt{8}\right)+\left(-\dfrac{49}{6}\right)\sqrt{8}\right)+\left(4\right)\\
&=&\left(\left(\dfrac{63}{2}\right)\sqrt{2}+\left(-6\right)\sqrt{2}+\left(\dfrac{195}{2}\right)\sqrt{2}+\left(\left(\dfrac{195}{2}\right)\sqrt{2}\right)+3-\left(\left(-\dfrac{49}{3}\right)\sqrt{2}\right)+\left(-\dfrac{49}{3}\right)\sqrt{2}\right)+\left(4\right)\\
&=&\left(\dfrac{63}{2}\right)\sqrt{2}+\left(-6\right)\sqrt{2}+\left(\dfrac{195}{2}\right)\sqrt{2}+\left(\left(\dfrac{195}{2}\right)\sqrt{2}\right)+3-\left(\left(-\dfrac{49}{3}\right)\sqrt{2}\right)+\left(-\dfrac{49}{3}\right)\sqrt{2}+4\\
&=&\left(\dfrac{441}{2}\right)\sqrt{2}+7\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\dfrac{21}{2}\right)\sqrt{18}+\left(-\dfrac{6}{5}\right)\sqrt{50}+\left(\dfrac{39}{2}\right)\sqrt{50}+\left(\left(\dfrac{39}{2}\right)\sqrt{50}\right)-\left(\left(-\dfrac{3}{2}\right)\sqrt{4}\right)-\left(\left(-\dfrac{49}{6}\right)\sqrt{8}\right)+\left(-\dfrac{49}{6}\right)\sqrt{8}\right)-\left(4\right)\\
&=&\left(\left(\dfrac{63}{2}\right)\sqrt{2}+\left(-6\right)\sqrt{2}+\left(\dfrac{195}{2}\right)\sqrt{2}+\left(\left(\dfrac{195}{2}\right)\sqrt{2}\right)+3-\left(\left(-\dfrac{49}{3}\right)\sqrt{2}\right)+\left(-\dfrac{49}{3}\right)\sqrt{2}\right)-\left(4\right)\\
&=&\left(\left(\dfrac{441}{2}\right)\sqrt{2}+3\right)-\left(4\right)\\
&=&\left(\dfrac{441}{2}\right)\sqrt{2}+3+-4\\
&=&\left(\dfrac{441}{2}\right)\sqrt{2}-1\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\dfrac{21}{2}\right)\sqrt{18}+\left(-\dfrac{6}{5}\right)\sqrt{50}+\left(\dfrac{39}{2}\right)\sqrt{50}+\left(\left(\dfrac{39}{2}\right)\sqrt{50}\right)-\left(\left(-\dfrac{3}{2}\right)\sqrt{4}\right)-\left(\left(-\dfrac{49}{6}\right)\sqrt{8}\right)+\left(-\dfrac{49}{6}\right)\sqrt{8}\right)\times\left(4\right)\\
&=&\left(\left(\dfrac{63}{2}\right)\sqrt{2}+\left(-6\right)\sqrt{2}+\left(\dfrac{195}{2}\right)\sqrt{2}+\left(\left(\dfrac{195}{2}\right)\sqrt{2}\right)+3-\left(\left(-\dfrac{49}{3}\right)\sqrt{2}\right)+\left(-\dfrac{49}{3}\right)\sqrt{2}\right)\times\left(4\right)\\
&=&\left(\left(\dfrac{441}{2}\right)\sqrt{2}+3\right)\left(4\right)\\
&=&\left(882\right)\sqrt{2}+12\\
&=&\left(882\right)\sqrt{2}+12\\
\end{eqnarray*}