L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(\dfrac{7}{9}\right)\sqrt{50}\) et \( Y=\left(\left(6\right)\sqrt{8}\right)-\left(\left(-6\right)\sqrt{18}\right)-\left(\left(-6\right)\sqrt{18}\right)-\left(\left(\dfrac{9}{5}\right)\sqrt{50}\right)+\left(-\dfrac{7}{2}\right)\sqrt{50}+\left(\left(-8\right)\sqrt{4}\right)-\left(\left(-\dfrac{26}{7}\right)\sqrt{50}\right)\) . 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{7}{9}\right)\sqrt{50}\right)+\left(\left(\left(6\right)\sqrt{8}\right)-\left(\left(-6\right)\sqrt{18}\right)-\left(\left(-6\right)\sqrt{18}\right)-\left(\left(\dfrac{9}{5}\right)\sqrt{50}\right)+\left(-\dfrac{7}{2}\right)\sqrt{50}+\left(\left(-8\right)\sqrt{4}\right)-\left(\left(-\dfrac{26}{7}\right)\sqrt{50}\right)\right)\\
&=&\left(\left(\dfrac{35}{9}\right)\sqrt{2}\right)+\left(\left(\left(12\right)\sqrt{2}\right)-\left(\left(-18\right)\sqrt{2}\right)-\left(\left(-18\right)\sqrt{2}\right)-\left(\left(9\right)\sqrt{2}\right)+\left(-\dfrac{35}{2}\right)\sqrt{2}-16-\left(\left(-\dfrac{130}{7}\right)\sqrt{2}\right)\right)\\
&=&\left(\dfrac{35}{9}\right)\sqrt{2}+\left(\left(12\right)\sqrt{2}\right)-\left(\left(-18\right)\sqrt{2}\right)-\left(\left(-18\right)\sqrt{2}\right)-\left(\left(9\right)\sqrt{2}\right)+\left(-\dfrac{35}{2}\right)\sqrt{2}-16-\left(\left(-\dfrac{130}{7}\right)\sqrt{2}\right)\\
&=&\left(\dfrac{5539}{126}\right)\sqrt{2}-16\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\dfrac{7}{9}\right)\sqrt{50}\right)-\left(\left(\left(6\right)\sqrt{8}\right)-\left(\left(-6\right)\sqrt{18}\right)-\left(\left(-6\right)\sqrt{18}\right)-\left(\left(\dfrac{9}{5}\right)\sqrt{50}\right)+\left(-\dfrac{7}{2}\right)\sqrt{50}+\left(\left(-8\right)\sqrt{4}\right)-\left(\left(-\dfrac{26}{7}\right)\sqrt{50}\right)\right)\\
&=&\left(\left(\dfrac{35}{9}\right)\sqrt{2}\right)-\left(\left(\left(12\right)\sqrt{2}\right)-\left(\left(-18\right)\sqrt{2}\right)-\left(\left(-18\right)\sqrt{2}\right)-\left(\left(9\right)\sqrt{2}\right)+\left(-\dfrac{35}{2}\right)\sqrt{2}-16-\left(\left(-\dfrac{130}{7}\right)\sqrt{2}\right)\right)\\
&=&\left(\left(\dfrac{35}{9}\right)\sqrt{2}\right)-\left(\left(\dfrac{561}{14}\right)\sqrt{2}-16\right)\\
&=&\left(\dfrac{35}{9}\right)\sqrt{2}+\left(-\dfrac{561}{14}\right)\sqrt{2}+16\\
&=&\left(-\dfrac{4559}{126}\right)\sqrt{2}+16\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\dfrac{7}{9}\right)\sqrt{50}\right)\times\left(\left(\left(6\right)\sqrt{8}\right)-\left(\left(-6\right)\sqrt{18}\right)-\left(\left(-6\right)\sqrt{18}\right)-\left(\left(\dfrac{9}{5}\right)\sqrt{50}\right)+\left(-\dfrac{7}{2}\right)\sqrt{50}+\left(\left(-8\right)\sqrt{4}\right)-\left(\left(-\dfrac{26}{7}\right)\sqrt{50}\right)\right)\\
&=&\left(\left(\dfrac{35}{9}\right)\sqrt{2}\right)\times\left(\left(\left(12\right)\sqrt{2}\right)-\left(\left(-18\right)\sqrt{2}\right)-\left(\left(-18\right)\sqrt{2}\right)-\left(\left(9\right)\sqrt{2}\right)+\left(-\dfrac{35}{2}\right)\sqrt{2}-16-\left(\left(-\dfrac{130}{7}\right)\sqrt{2}\right)\right)\\
&=&\left(\left(\dfrac{35}{9}\right)\sqrt{2}\right)\left(\left(\dfrac{561}{14}\right)\sqrt{2}-16\right)\\
&=&\left(\dfrac{935}{6}\right)\sqrt{4}+\left(-\dfrac{560}{9}\right)\sqrt{2}\\
&=&\dfrac{935}{3}+\left(-\dfrac{560}{9}\right)\sqrt{2}\\
\end{eqnarray*}