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 \( X=\dfrac{71}{5}-\dfrac{74}{3}+\left(\left(\dfrac{14}{5}\right)\sqrt{45}\right)-\left(\left(-\dfrac{7}{5}\right)\sqrt{25}\right)-\left(\left(-2\right)\sqrt{20}\right)+\dfrac{23}{4}\) et \( Y=\left(5\right)\sqrt{20}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\dfrac{71}{5}-\dfrac{74}{3}+\left(\left(\dfrac{14}{5}\right)\sqrt{45}\right)-\left(\left(-\dfrac{7}{5}\right)\sqrt{25}\right)-\left(\left(-2\right)\sqrt{20}\right)+\dfrac{23}{4}\right)+\left(\left(5\right)\sqrt{20}\right)\\
&=&\left(\dfrac{71}{5}-\dfrac{74}{3}+\left(\left(\dfrac{42}{5}\right)\sqrt{5}\right)+7-\left(\left(-4\right)\sqrt{5}\right)+\dfrac{23}{4}\right)+\left(\left(10\right)\sqrt{5}\right)\\
&=&\dfrac{71}{5}-\dfrac{74}{3}+\left(\left(\dfrac{42}{5}\right)\sqrt{5}\right)+7-\left(\left(-4\right)\sqrt{5}\right)+\dfrac{23}{4}+\left(10\right)\sqrt{5}\\
&=&\dfrac{137}{60}+\left(\dfrac{112}{5}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\dfrac{71}{5}-\dfrac{74}{3}+\left(\left(\dfrac{14}{5}\right)\sqrt{45}\right)-\left(\left(-\dfrac{7}{5}\right)\sqrt{25}\right)-\left(\left(-2\right)\sqrt{20}\right)+\dfrac{23}{4}\right)-\left(\left(5\right)\sqrt{20}\right)\\
&=&\left(\dfrac{71}{5}-\dfrac{74}{3}+\left(\left(\dfrac{42}{5}\right)\sqrt{5}\right)+7-\left(\left(-4\right)\sqrt{5}\right)+\dfrac{23}{4}\right)-\left(\left(10\right)\sqrt{5}\right)\\
&=&\left(\dfrac{137}{60}+\left(\dfrac{62}{5}\right)\sqrt{5}\right)-\left(\left(10\right)\sqrt{5}\right)\\
&=&\dfrac{137}{60}+\left(\dfrac{62}{5}\right)\sqrt{5}+\left(-10\right)\sqrt{5}\\
&=&\dfrac{137}{60}+\left(\dfrac{12}{5}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\dfrac{71}{5}-\dfrac{74}{3}+\left(\left(\dfrac{14}{5}\right)\sqrt{45}\right)-\left(\left(-\dfrac{7}{5}\right)\sqrt{25}\right)-\left(\left(-2\right)\sqrt{20}\right)+\dfrac{23}{4}\right)\times\left(\left(5\right)\sqrt{20}\right)\\
&=&\left(\dfrac{71}{5}-\dfrac{74}{3}+\left(\left(\dfrac{42}{5}\right)\sqrt{5}\right)+7-\left(\left(-4\right)\sqrt{5}\right)+\dfrac{23}{4}\right)\times\left(\left(10\right)\sqrt{5}\right)\\
&=&\left(\dfrac{137}{60}+\left(\dfrac{62}{5}\right)\sqrt{5}\right)\left(\left(10\right)\sqrt{5}\right)\\
&=&\left(\dfrac{137}{6}\right)\sqrt{5}+\left(124\right)\sqrt{25}\\
&=&\left(\dfrac{137}{6}\right)\sqrt{5}+620\\
\end{eqnarray*}