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 \( X=\left(-\dfrac{9}{5}\right)\sqrt{20}\) et \( Y=\left(-\dfrac{49}{4}\right)\sqrt{25}+0-\left(\left(3\right)\sqrt{25}\right)-4-\left(\left(-\dfrac{55}{7}\right)\sqrt{45}\right)+\left(-\dfrac{49}{4}\right)\sqrt{25}\) . 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{9}{5}\right)\sqrt{20}\right)+\left(\left(-\dfrac{49}{4}\right)\sqrt{25}+0-\left(\left(3\right)\sqrt{25}\right)-4-\left(\left(-\dfrac{55}{7}\right)\sqrt{45}\right)+\left(-\dfrac{49}{4}\right)\sqrt{25}\right)\\
&=&\left(\left(-\dfrac{18}{5}\right)\sqrt{5}\right)+\left(-\dfrac{245}{4}+0-15-4-\left(\left(-\dfrac{165}{7}\right)\sqrt{5}\right)-\dfrac{245}{4}\right)\\
&=&\left(-\dfrac{18}{5}\right)\sqrt{5}-\dfrac{245}{4}+0-15-4-\left(\left(-\dfrac{165}{7}\right)\sqrt{5}\right)-\dfrac{245}{4}\\
&=&\left(\dfrac{699}{35}\right)\sqrt{5}-\dfrac{283}{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{9}{5}\right)\sqrt{20}\right)-\left(\left(-\dfrac{49}{4}\right)\sqrt{25}+0-\left(\left(3\right)\sqrt{25}\right)-4-\left(\left(-\dfrac{55}{7}\right)\sqrt{45}\right)+\left(-\dfrac{49}{4}\right)\sqrt{25}\right)\\
&=&\left(\left(-\dfrac{18}{5}\right)\sqrt{5}\right)-\left(-\dfrac{245}{4}+0-15-4-\left(\left(-\dfrac{165}{7}\right)\sqrt{5}\right)-\dfrac{245}{4}\right)\\
&=&\left(\left(-\dfrac{18}{5}\right)\sqrt{5}\right)-\left(-\dfrac{283}{2}+\left(\dfrac{165}{7}\right)\sqrt{5}\right)\\
&=&\left(-\dfrac{18}{5}\right)\sqrt{5}+\dfrac{283}{2}+\left(-\dfrac{165}{7}\right)\sqrt{5}\\
&=&\left(-\dfrac{951}{35}\right)\sqrt{5}+\dfrac{283}{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{9}{5}\right)\sqrt{20}\right)\times\left(\left(-\dfrac{49}{4}\right)\sqrt{25}+0-\left(\left(3\right)\sqrt{25}\right)-4-\left(\left(-\dfrac{55}{7}\right)\sqrt{45}\right)+\left(-\dfrac{49}{4}\right)\sqrt{25}\right)\\
&=&\left(\left(-\dfrac{18}{5}\right)\sqrt{5}\right)\times\left(-\dfrac{245}{4}+0-15-4-\left(\left(-\dfrac{165}{7}\right)\sqrt{5}\right)-\dfrac{245}{4}\right)\\
&=&\left(\left(-\dfrac{18}{5}\right)\sqrt{5}\right)\left(-\dfrac{283}{2}+\left(\dfrac{165}{7}\right)\sqrt{5}\right)\\
&=&\left(\dfrac{2547}{5}\right)\sqrt{5}+\left(-\dfrac{594}{7}\right)\sqrt{25}\\
&=&\left(\dfrac{2547}{5}\right)\sqrt{5}-\dfrac{2970}{7}\\
\end{eqnarray*}