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 \( X=\left(\dfrac{41}{3}\right)\sqrt{45}\) et \( Y=\left(\dfrac{79}{9}\right)\sqrt{125}+\left(-\dfrac{64}{3}\right)\sqrt{20}+\left(\left(-7\right)\sqrt{125}\right)-\left(\left(-\dfrac{19}{2}\right)\sqrt{20}\right)-\left(\left(0\right)\sqrt{45}\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(\dfrac{41}{3}\right)\sqrt{45}\right)+\left(\left(\dfrac{79}{9}\right)\sqrt{125}+\left(-\dfrac{64}{3}\right)\sqrt{20}+\left(\left(-7\right)\sqrt{125}\right)-\left(\left(-\dfrac{19}{2}\right)\sqrt{20}\right)-\left(\left(0\right)\sqrt{45}\right)\right)\\
&=&\left(\left(41\right)\sqrt{5}\right)+\left(\left(\dfrac{395}{9}\right)\sqrt{5}+\left(-\dfrac{128}{3}\right)\sqrt{5}+\left(\left(-35\right)\sqrt{5}\right)-\left(\left(-19\right)\sqrt{5}\right)-\left(\left(0\right)\sqrt{5}\right)\right)\\
&=&\left(41\right)\sqrt{5}+\left(\dfrac{395}{9}\right)\sqrt{5}+\left(-\dfrac{128}{3}\right)\sqrt{5}+\left(\left(-35\right)\sqrt{5}\right)-\left(\left(-19\right)\sqrt{5}\right)-\left(\left(0\right)\sqrt{5}\right)\\
&=&\left(\dfrac{236}{9}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\dfrac{41}{3}\right)\sqrt{45}\right)-\left(\left(\dfrac{79}{9}\right)\sqrt{125}+\left(-\dfrac{64}{3}\right)\sqrt{20}+\left(\left(-7\right)\sqrt{125}\right)-\left(\left(-\dfrac{19}{2}\right)\sqrt{20}\right)-\left(\left(0\right)\sqrt{45}\right)\right)\\
&=&\left(\left(41\right)\sqrt{5}\right)-\left(\left(\dfrac{395}{9}\right)\sqrt{5}+\left(-\dfrac{128}{3}\right)\sqrt{5}+\left(\left(-35\right)\sqrt{5}\right)-\left(\left(-19\right)\sqrt{5}\right)-\left(\left(0\right)\sqrt{5}\right)\right)\\
&=&\left(\left(41\right)\sqrt{5}\right)-\left(\left(-\dfrac{133}{9}\right)\sqrt{5}\right)\\
&=&\left(41\right)\sqrt{5}+\left(\dfrac{133}{9}\right)\sqrt{5}\\
&=&\left(\dfrac{502}{9}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\dfrac{41}{3}\right)\sqrt{45}\right)\times\left(\left(\dfrac{79}{9}\right)\sqrt{125}+\left(-\dfrac{64}{3}\right)\sqrt{20}+\left(\left(-7\right)\sqrt{125}\right)-\left(\left(-\dfrac{19}{2}\right)\sqrt{20}\right)-\left(\left(0\right)\sqrt{45}\right)\right)\\
&=&\left(\left(41\right)\sqrt{5}\right)\times\left(\left(\dfrac{395}{9}\right)\sqrt{5}+\left(-\dfrac{128}{3}\right)\sqrt{5}+\left(\left(-35\right)\sqrt{5}\right)-\left(\left(-19\right)\sqrt{5}\right)-\left(\left(0\right)\sqrt{5}\right)\right)\\
&=&\left(\left(41\right)\sqrt{5}\right)\left(\left(-\dfrac{133}{9}\right)\sqrt{5}\right)\\
&=&\left(-\dfrac{5453}{9}\right)\sqrt{25}\\
&=&-\dfrac{27265}{9}\\
\end{eqnarray*}