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 \( X=-\dfrac{8}{9}+\left(-\dfrac{34}{7}\right)\sqrt{4}+\left(3\right)\sqrt{4}+6+\left(8\right)\sqrt{4}+\left(\dfrac{1}{2}\right)\sqrt{8}+\left(-\dfrac{49}{2}\right)\sqrt{50}+\left(\left(-\dfrac{60}{7}\right)\sqrt{8}\right)-\left(\left(\dfrac{4}{5}\right)\sqrt{50}\right)\) et \( Y=-\dfrac{67}{3}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(-\dfrac{8}{9}+\left(-\dfrac{34}{7}\right)\sqrt{4}+\left(3\right)\sqrt{4}+6+\left(8\right)\sqrt{4}+\left(\dfrac{1}{2}\right)\sqrt{8}+\left(-\dfrac{49}{2}\right)\sqrt{50}+\left(\left(-\dfrac{60}{7}\right)\sqrt{8}\right)-\left(\left(\dfrac{4}{5}\right)\sqrt{50}\right)\right)+\left(-\dfrac{67}{3}\right)\\
&=&\left(-\dfrac{8}{9}-\dfrac{68}{7}+6+6+16+\left(1\right)\sqrt{2}+\left(-\dfrac{245}{2}\right)\sqrt{2}+\left(\left(-\dfrac{120}{7}\right)\sqrt{2}\right)-\left(\left(4\right)\sqrt{2}\right)\right)+\left(-\dfrac{67}{3}\right)\\
&=&-\dfrac{8}{9}-\dfrac{68}{7}+6+6+16+\left(1\right)\sqrt{2}+\left(-\dfrac{245}{2}\right)\sqrt{2}+\left(\left(-\dfrac{120}{7}\right)\sqrt{2}\right)-\left(\left(4\right)\sqrt{2}\right)-\dfrac{67}{3}\\
&=&-\dfrac{311}{63}+\left(-\dfrac{1997}{14}\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(-\dfrac{8}{9}+\left(-\dfrac{34}{7}\right)\sqrt{4}+\left(3\right)\sqrt{4}+6+\left(8\right)\sqrt{4}+\left(\dfrac{1}{2}\right)\sqrt{8}+\left(-\dfrac{49}{2}\right)\sqrt{50}+\left(\left(-\dfrac{60}{7}\right)\sqrt{8}\right)-\left(\left(\dfrac{4}{5}\right)\sqrt{50}\right)\right)-\left(-\dfrac{67}{3}\right)\\
&=&\left(-\dfrac{8}{9}-\dfrac{68}{7}+6+6+16+\left(1\right)\sqrt{2}+\left(-\dfrac{245}{2}\right)\sqrt{2}+\left(\left(-\dfrac{120}{7}\right)\sqrt{2}\right)-\left(\left(4\right)\sqrt{2}\right)\right)-\left(-\dfrac{67}{3}\right)\\
&=&\left(\dfrac{1096}{63}+\left(-\dfrac{1997}{14}\right)\sqrt{2}\right)-\left(-\dfrac{67}{3}\right)\\
&=&\dfrac{1096}{63}+\left(-\dfrac{1997}{14}\right)\sqrt{2}+\dfrac{67}{3}\\
&=&\dfrac{2503}{63}+\left(-\dfrac{1997}{14}\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(-\dfrac{8}{9}+\left(-\dfrac{34}{7}\right)\sqrt{4}+\left(3\right)\sqrt{4}+6+\left(8\right)\sqrt{4}+\left(\dfrac{1}{2}\right)\sqrt{8}+\left(-\dfrac{49}{2}\right)\sqrt{50}+\left(\left(-\dfrac{60}{7}\right)\sqrt{8}\right)-\left(\left(\dfrac{4}{5}\right)\sqrt{50}\right)\right)\times\left(-\dfrac{67}{3}\right)\\
&=&\left(-\dfrac{8}{9}-\dfrac{68}{7}+6+6+16+\left(1\right)\sqrt{2}+\left(-\dfrac{245}{2}\right)\sqrt{2}+\left(\left(-\dfrac{120}{7}\right)\sqrt{2}\right)-\left(\left(4\right)\sqrt{2}\right)\right)\times\left(-\dfrac{67}{3}\right)\\
&=&\left(\dfrac{1096}{63}+\left(-\dfrac{1997}{14}\right)\sqrt{2}\right)\left(-\dfrac{67}{3}\right)\\
&=&-\dfrac{73432}{189}+\left(\dfrac{133799}{42}\right)\sqrt{2}\\
&=&-\dfrac{73432}{189}+\left(\dfrac{133799}{42}\right)\sqrt{2}\\
\end{eqnarray*}