L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
Si vous regénérez la page (F5) les valeurs seront changées.
La correction se trouve en bas de page.
Exercice
Soit \( X=\left(-\dfrac{65}{8}\right)\sqrt{50}\) et \( Y=\left(3\right)\sqrt{8}+\left(\dfrac{46}{7}\right)\sqrt{4}+\left(-\dfrac{80}{7}\right)\sqrt{8}+\left(\left(0\right)\sqrt{18}\right)-\left(\left(-\dfrac{25}{2}\right)\sqrt{4}\right)-\left(\left(\dfrac{55}{9}\right)\sqrt{18}\right)\) . 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{65}{8}\right)\sqrt{50}\right)+\left(\left(3\right)\sqrt{8}+\left(\dfrac{46}{7}\right)\sqrt{4}+\left(-\dfrac{80}{7}\right)\sqrt{8}+\left(\left(0\right)\sqrt{18}\right)-\left(\left(-\dfrac{25}{2}\right)\sqrt{4}\right)-\left(\left(\dfrac{55}{9}\right)\sqrt{18}\right)\right)\\
&=&\left(\left(-\dfrac{325}{8}\right)\sqrt{2}\right)+\left(\left(6\right)\sqrt{2}+\dfrac{92}{7}+\left(-\dfrac{160}{7}\right)\sqrt{2}+\left(\left(0\right)\sqrt{2}\right)+25-\left(\left(\dfrac{55}{3}\right)\sqrt{2}\right)\right)\\
&=&\left(-\dfrac{325}{8}\right)\sqrt{2}+\left(6\right)\sqrt{2}+\dfrac{92}{7}+\left(-\dfrac{160}{7}\right)\sqrt{2}+\left(\left(0\right)\sqrt{2}\right)+25-\left(\left(\dfrac{55}{3}\right)\sqrt{2}\right)\\
&=&\left(-\dfrac{12737}{168}\right)\sqrt{2}+\dfrac{267}{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{65}{8}\right)\sqrt{50}\right)-\left(\left(3\right)\sqrt{8}+\left(\dfrac{46}{7}\right)\sqrt{4}+\left(-\dfrac{80}{7}\right)\sqrt{8}+\left(\left(0\right)\sqrt{18}\right)-\left(\left(-\dfrac{25}{2}\right)\sqrt{4}\right)-\left(\left(\dfrac{55}{9}\right)\sqrt{18}\right)\right)\\
&=&\left(\left(-\dfrac{325}{8}\right)\sqrt{2}\right)-\left(\left(6\right)\sqrt{2}+\dfrac{92}{7}+\left(-\dfrac{160}{7}\right)\sqrt{2}+\left(\left(0\right)\sqrt{2}\right)+25-\left(\left(\dfrac{55}{3}\right)\sqrt{2}\right)\right)\\
&=&\left(\left(-\dfrac{325}{8}\right)\sqrt{2}\right)-\left(\left(-\dfrac{739}{21}\right)\sqrt{2}+\dfrac{267}{7}\right)\\
&=&\left(-\dfrac{325}{8}\right)\sqrt{2}+\left(\dfrac{739}{21}\right)\sqrt{2}-\dfrac{267}{7}\\
&=&\left(-\dfrac{913}{168}\right)\sqrt{2}-\dfrac{267}{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{65}{8}\right)\sqrt{50}\right)\times\left(\left(3\right)\sqrt{8}+\left(\dfrac{46}{7}\right)\sqrt{4}+\left(-\dfrac{80}{7}\right)\sqrt{8}+\left(\left(0\right)\sqrt{18}\right)-\left(\left(-\dfrac{25}{2}\right)\sqrt{4}\right)-\left(\left(\dfrac{55}{9}\right)\sqrt{18}\right)\right)\\
&=&\left(\left(-\dfrac{325}{8}\right)\sqrt{2}\right)\times\left(\left(6\right)\sqrt{2}+\dfrac{92}{7}+\left(-\dfrac{160}{7}\right)\sqrt{2}+\left(\left(0\right)\sqrt{2}\right)+25-\left(\left(\dfrac{55}{3}\right)\sqrt{2}\right)\right)\\
&=&\left(\left(-\dfrac{325}{8}\right)\sqrt{2}\right)\left(\left(-\dfrac{739}{21}\right)\sqrt{2}+\dfrac{267}{7}\right)\\
&=&\left(\dfrac{240175}{168}\right)\sqrt{4}+\left(-\dfrac{86775}{56}\right)\sqrt{2}\\
&=&\dfrac{240175}{84}+\left(-\dfrac{86775}{56}\right)\sqrt{2}\\
\end{eqnarray*}