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 \( X=\left(-\dfrac{14}{5}\right)\sqrt{18}+\left(\left(-\dfrac{14}{5}\right)\sqrt{18}\right)-\left(\left(1\right)\sqrt{4}\right)+\left(5\right)\sqrt{8}+\left(\dfrac{29}{4}\right)\sqrt{18}\) et \( Y=-\dfrac{55}{9}\) . 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{14}{5}\right)\sqrt{18}+\left(\left(-\dfrac{14}{5}\right)\sqrt{18}\right)-\left(\left(1\right)\sqrt{4}\right)+\left(5\right)\sqrt{8}+\left(\dfrac{29}{4}\right)\sqrt{18}\right)+\left(-\dfrac{55}{9}\right)\\
&=&\left(\left(-\dfrac{42}{5}\right)\sqrt{2}+\left(\left(-\dfrac{42}{5}\right)\sqrt{2}\right)-2+\left(10\right)\sqrt{2}+\left(\dfrac{87}{4}\right)\sqrt{2}\right)+\left(-\dfrac{55}{9}\right)\\
&=&\left(-\dfrac{42}{5}\right)\sqrt{2}+\left(\left(-\dfrac{42}{5}\right)\sqrt{2}\right)-2+\left(10\right)\sqrt{2}+\left(\dfrac{87}{4}\right)\sqrt{2}-\dfrac{55}{9}\\
&=&\left(\dfrac{299}{20}\right)\sqrt{2}-\dfrac{73}{9}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{14}{5}\right)\sqrt{18}+\left(\left(-\dfrac{14}{5}\right)\sqrt{18}\right)-\left(\left(1\right)\sqrt{4}\right)+\left(5\right)\sqrt{8}+\left(\dfrac{29}{4}\right)\sqrt{18}\right)-\left(-\dfrac{55}{9}\right)\\
&=&\left(\left(-\dfrac{42}{5}\right)\sqrt{2}+\left(\left(-\dfrac{42}{5}\right)\sqrt{2}\right)-2+\left(10\right)\sqrt{2}+\left(\dfrac{87}{4}\right)\sqrt{2}\right)-\left(-\dfrac{55}{9}\right)\\
&=&\left(\left(\dfrac{299}{20}\right)\sqrt{2}-2\right)-\left(-\dfrac{55}{9}\right)\\
&=&\left(\dfrac{299}{20}\right)\sqrt{2}-2+\dfrac{55}{9}\\
&=&\left(\dfrac{299}{20}\right)\sqrt{2}+\dfrac{37}{9}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{14}{5}\right)\sqrt{18}+\left(\left(-\dfrac{14}{5}\right)\sqrt{18}\right)-\left(\left(1\right)\sqrt{4}\right)+\left(5\right)\sqrt{8}+\left(\dfrac{29}{4}\right)\sqrt{18}\right)\times\left(-\dfrac{55}{9}\right)\\
&=&\left(\left(-\dfrac{42}{5}\right)\sqrt{2}+\left(\left(-\dfrac{42}{5}\right)\sqrt{2}\right)-2+\left(10\right)\sqrt{2}+\left(\dfrac{87}{4}\right)\sqrt{2}\right)\times\left(-\dfrac{55}{9}\right)\\
&=&\left(\left(\dfrac{299}{20}\right)\sqrt{2}-2\right)\left(-\dfrac{55}{9}\right)\\
&=&\left(-\dfrac{3289}{36}\right)\sqrt{2}+\dfrac{110}{9}\\
&=&\left(-\dfrac{3289}{36}\right)\sqrt{2}+\dfrac{110}{9}\\
\end{eqnarray*}