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 \( X=\left(-4\right)\sqrt{50}\) et \( Y=\left(\left(4\right)\sqrt{18}+\left(6\right)\sqrt{4}+\left(\dfrac{73}{5}\right)\sqrt{18}\right)-\left(\left(\left(-\dfrac{10}{3}\right)\sqrt{8}\right)-\left(\left(\dfrac{33}{5}\right)\sqrt{4}\right)-\left(\left(\dfrac{10}{9}\right)\sqrt{50}\right)\right)-\left(\left(6\right)\sqrt{4}\right)-\left(\left(4\right)\sqrt{18}\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(-4\right)\sqrt{50}\right)+\left(\left(\left(4\right)\sqrt{18}+\left(6\right)\sqrt{4}+\left(\dfrac{73}{5}\right)\sqrt{18}\right)-\left(\left(\left(-\dfrac{10}{3}\right)\sqrt{8}\right)-\left(\left(\dfrac{33}{5}\right)\sqrt{4}\right)-\left(\left(\dfrac{10}{9}\right)\sqrt{50}\right)\right)-\left(\left(6\right)\sqrt{4}\right)-\left(\left(4\right)\sqrt{18}\right)\right)\\
&=&\left(\left(-20\right)\sqrt{2}\right)+\left(\left(\left(12\right)\sqrt{2}+12+\left(\dfrac{219}{5}\right)\sqrt{2}\right)-\left(\left(\left(-\dfrac{20}{3}\right)\sqrt{2}\right)-\dfrac{66}{5}-\left(\left(\dfrac{50}{9}\right)\sqrt{2}\right)\right)-12-\left(\left(12\right)\sqrt{2}\right)\right)\\
&=&\left(-20\right)\sqrt{2}+\left(\left(12\right)\sqrt{2}+12+\left(\dfrac{219}{5}\right)\sqrt{2}\right)-\left(\left(\left(-\dfrac{20}{3}\right)\sqrt{2}\right)-\dfrac{66}{5}-\left(\left(\dfrac{50}{9}\right)\sqrt{2}\right)\right)-12-\left(\left(12\right)\sqrt{2}\right)\\
&=&\left(\dfrac{1621}{45}\right)\sqrt{2}+\dfrac{66}{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-4\right)\sqrt{50}\right)-\left(\left(\left(4\right)\sqrt{18}+\left(6\right)\sqrt{4}+\left(\dfrac{73}{5}\right)\sqrt{18}\right)-\left(\left(\left(-\dfrac{10}{3}\right)\sqrt{8}\right)-\left(\left(\dfrac{33}{5}\right)\sqrt{4}\right)-\left(\left(\dfrac{10}{9}\right)\sqrt{50}\right)\right)-\left(\left(6\right)\sqrt{4}\right)-\left(\left(4\right)\sqrt{18}\right)\right)\\
&=&\left(\left(-20\right)\sqrt{2}\right)-\left(\left(\left(12\right)\sqrt{2}+12+\left(\dfrac{219}{5}\right)\sqrt{2}\right)-\left(\left(\left(-\dfrac{20}{3}\right)\sqrt{2}\right)-\dfrac{66}{5}-\left(\left(\dfrac{50}{9}\right)\sqrt{2}\right)\right)-12-\left(\left(12\right)\sqrt{2}\right)\right)\\
&=&\left(\left(-20\right)\sqrt{2}\right)-\left(\left(\dfrac{2521}{45}\right)\sqrt{2}+\dfrac{66}{5}\right)\\
&=&\left(-20\right)\sqrt{2}+\left(-\dfrac{2521}{45}\right)\sqrt{2}-\dfrac{66}{5}\\
&=&\left(-\dfrac{3421}{45}\right)\sqrt{2}-\dfrac{66}{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-4\right)\sqrt{50}\right)\times\left(\left(\left(4\right)\sqrt{18}+\left(6\right)\sqrt{4}+\left(\dfrac{73}{5}\right)\sqrt{18}\right)-\left(\left(\left(-\dfrac{10}{3}\right)\sqrt{8}\right)-\left(\left(\dfrac{33}{5}\right)\sqrt{4}\right)-\left(\left(\dfrac{10}{9}\right)\sqrt{50}\right)\right)-\left(\left(6\right)\sqrt{4}\right)-\left(\left(4\right)\sqrt{18}\right)\right)\\
&=&\left(\left(-20\right)\sqrt{2}\right)\times\left(\left(\left(12\right)\sqrt{2}+12+\left(\dfrac{219}{5}\right)\sqrt{2}\right)-\left(\left(\left(-\dfrac{20}{3}\right)\sqrt{2}\right)-\dfrac{66}{5}-\left(\left(\dfrac{50}{9}\right)\sqrt{2}\right)\right)-12-\left(\left(12\right)\sqrt{2}\right)\right)\\
&=&\left(\left(-20\right)\sqrt{2}\right)\left(\left(\dfrac{2521}{45}\right)\sqrt{2}+\dfrac{66}{5}\right)\\
&=&\left(-\dfrac{10084}{9}\right)\sqrt{4}+\left(-264\right)\sqrt{2}\\
&=&-\dfrac{20168}{9}+\left(-264\right)\sqrt{2}\\
\end{eqnarray*}