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 \(  X=\left(0\right)\sqrt{8}+\left(-\dfrac{26}{5}\right)\sqrt{18}+\left(\dfrac{31}{3}\right)\sqrt{50}+\left(-\dfrac{41}{3}\right)\sqrt{50}\)  et \(  Y=\left(-\dfrac{23}{4}\right)\sqrt{18}\) . Calculer et simplifier \(  X+Y\) , \(  X-Y\)  et \(  X\times Y\) .
		
Cliquer ici pour afficher la solution
Exercice 
		
\begin{eqnarray*}
		X+Y
		&=&\left(\left(0\right)\sqrt{8}+\left(-\dfrac{26}{5}\right)\sqrt{18}+\left(\dfrac{31}{3}\right)\sqrt{50}+\left(-\dfrac{41}{3}\right)\sqrt{50}\right)+\left(\left(-\dfrac{23}{4}\right)\sqrt{18}\right)\\
		&=&\left(\left(0\right)\sqrt{2}+\left(-\dfrac{78}{5}\right)\sqrt{2}+\left(\dfrac{155}{3}\right)\sqrt{2}+\left(-\dfrac{205}{3}\right)\sqrt{2}\right)+\left(\left(-\dfrac{69}{4}\right)\sqrt{2}\right)\\
		&=&\left(0\right)\sqrt{2}+\left(-\dfrac{78}{5}\right)\sqrt{2}+\left(\dfrac{155}{3}\right)\sqrt{2}+\left(-\dfrac{205}{3}\right)\sqrt{2}+\left(-\dfrac{69}{4}\right)\sqrt{2}\\
		&=&\left(-\dfrac{2971}{60}\right)\sqrt{2}\\
		\end{eqnarray*}
		
		
\begin{eqnarray*}
		X-Y
		&=&\left(\left(0\right)\sqrt{8}+\left(-\dfrac{26}{5}\right)\sqrt{18}+\left(\dfrac{31}{3}\right)\sqrt{50}+\left(-\dfrac{41}{3}\right)\sqrt{50}\right)-\left(\left(-\dfrac{23}{4}\right)\sqrt{18}\right)\\
		&=&\left(\left(0\right)\sqrt{2}+\left(-\dfrac{78}{5}\right)\sqrt{2}+\left(\dfrac{155}{3}\right)\sqrt{2}+\left(-\dfrac{205}{3}\right)\sqrt{2}\right)-\left(\left(-\dfrac{69}{4}\right)\sqrt{2}\right)\\
		&=&\left(\left(-\dfrac{484}{15}\right)\sqrt{2}\right)-\left(\left(-\dfrac{69}{4}\right)\sqrt{2}\right)\\
		&=&\left(-\dfrac{484}{15}\right)\sqrt{2}+\left(\dfrac{69}{4}\right)\sqrt{2}\\
		&=&\left(-\dfrac{901}{60}\right)\sqrt{2}\\
		\end{eqnarray*}
		
		
\begin{eqnarray*}
		X\times Y
		&=&\left(\left(0\right)\sqrt{8}+\left(-\dfrac{26}{5}\right)\sqrt{18}+\left(\dfrac{31}{3}\right)\sqrt{50}+\left(-\dfrac{41}{3}\right)\sqrt{50}\right)\times\left(\left(-\dfrac{23}{4}\right)\sqrt{18}\right)\\
		&=&\left(\left(0\right)\sqrt{2}+\left(-\dfrac{78}{5}\right)\sqrt{2}+\left(\dfrac{155}{3}\right)\sqrt{2}+\left(-\dfrac{205}{3}\right)\sqrt{2}\right)\times\left(\left(-\dfrac{69}{4}\right)\sqrt{2}\right)\\
		&=&\left(\left(-\dfrac{484}{15}\right)\sqrt{2}\right)\left(\left(-\dfrac{69}{4}\right)\sqrt{2}\right)\\
		&=&\left(\dfrac{2783}{5}\right)\sqrt{4}\\
		&=&\dfrac{5566}{5}\\
		\end{eqnarray*}