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 \( X=\left(\left(9\right)\sqrt{4}\right)-\left(\left(\left(0\right)\sqrt{50}\right)-\dfrac{39}{5}\right)\) et \( Y=\left(\dfrac{62}{5}\right)\sqrt{8}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(\left(9\right)\sqrt{4}\right)-\left(\left(\left(0\right)\sqrt{50}\right)-\dfrac{39}{5}\right)\right)+\left(\left(\dfrac{62}{5}\right)\sqrt{8}\right)\\
&=&\left(18-\left(\left(\left(0\right)\sqrt{2}\right)-\dfrac{39}{5}\right)\right)+\left(\left(\dfrac{124}{5}\right)\sqrt{2}\right)\\
&=&18-\left(\left(\left(0\right)\sqrt{2}\right)-\dfrac{39}{5}\right)+\left(\dfrac{124}{5}\right)\sqrt{2}\\
&=&\dfrac{129}{5}+\left(\dfrac{124}{5}\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(9\right)\sqrt{4}\right)-\left(\left(\left(0\right)\sqrt{50}\right)-\dfrac{39}{5}\right)\right)-\left(\left(\dfrac{62}{5}\right)\sqrt{8}\right)\\
&=&\left(18-\left(\left(\left(0\right)\sqrt{2}\right)-\dfrac{39}{5}\right)\right)-\left(\left(\dfrac{124}{5}\right)\sqrt{2}\right)\\
&=&\left(\dfrac{129}{5}+\left(0\right)\sqrt{2}\right)-\left(\left(\dfrac{124}{5}\right)\sqrt{2}\right)\\
&=&\dfrac{129}{5}+\left(0\right)\sqrt{2}+\left(-\dfrac{124}{5}\right)\sqrt{2}\\
&=&\dfrac{129}{5}+\left(-\dfrac{124}{5}\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(9\right)\sqrt{4}\right)-\left(\left(\left(0\right)\sqrt{50}\right)-\dfrac{39}{5}\right)\right)\times\left(\left(\dfrac{62}{5}\right)\sqrt{8}\right)\\
&=&\left(18-\left(\left(\left(0\right)\sqrt{2}\right)-\dfrac{39}{5}\right)\right)\times\left(\left(\dfrac{124}{5}\right)\sqrt{2}\right)\\
&=&\left(\dfrac{129}{5}+\left(0\right)\sqrt{2}\right)\left(\left(\dfrac{124}{5}\right)\sqrt{2}\right)\\
&=&\left(\dfrac{15996}{25}\right)\sqrt{2}+\left(0\right)\sqrt{4}\\
&=&\left(\dfrac{15996}{25}\right)\sqrt{2}+0\\
\end{eqnarray*}