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 \( X=-\dfrac{1}{8}+\left(\left(-8\right)\sqrt{50}\right)+\dfrac{79}{6}+\dfrac{43}{8}-\dfrac{29}{2}+\dfrac{29}{4}\) et \( Y=\dfrac{41}{7}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(-\dfrac{1}{8}+\left(\left(-8\right)\sqrt{50}\right)+\dfrac{79}{6}+\dfrac{43}{8}-\dfrac{29}{2}+\dfrac{29}{4}\right)+\left(\dfrac{41}{7}\right)\\
&=&\left(-\dfrac{1}{8}+\left(\left(-40\right)\sqrt{2}\right)+\dfrac{79}{6}+\dfrac{43}{8}-\dfrac{29}{2}+\dfrac{29}{4}\right)+\left(\dfrac{41}{7}\right)\\
&=&-\dfrac{1}{8}+\left(\left(-40\right)\sqrt{2}\right)+\dfrac{79}{6}+\dfrac{43}{8}-\dfrac{29}{2}+\dfrac{29}{4}+\dfrac{41}{7}\\
&=&\dfrac{715}{42}+\left(-40\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(-\dfrac{1}{8}+\left(\left(-8\right)\sqrt{50}\right)+\dfrac{79}{6}+\dfrac{43}{8}-\dfrac{29}{2}+\dfrac{29}{4}\right)-\left(\dfrac{41}{7}\right)\\
&=&\left(-\dfrac{1}{8}+\left(\left(-40\right)\sqrt{2}\right)+\dfrac{79}{6}+\dfrac{43}{8}-\dfrac{29}{2}+\dfrac{29}{4}\right)-\left(\dfrac{41}{7}\right)\\
&=&\left(\dfrac{67}{6}+\left(-40\right)\sqrt{2}\right)-\left(\dfrac{41}{7}\right)\\
&=&\dfrac{67}{6}+\left(-40\right)\sqrt{2}+-\dfrac{41}{7}\\
&=&\dfrac{223}{42}+\left(-40\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(-\dfrac{1}{8}+\left(\left(-8\right)\sqrt{50}\right)+\dfrac{79}{6}+\dfrac{43}{8}-\dfrac{29}{2}+\dfrac{29}{4}\right)\times\left(\dfrac{41}{7}\right)\\
&=&\left(-\dfrac{1}{8}+\left(\left(-40\right)\sqrt{2}\right)+\dfrac{79}{6}+\dfrac{43}{8}-\dfrac{29}{2}+\dfrac{29}{4}\right)\times\left(\dfrac{41}{7}\right)\\
&=&\left(\dfrac{67}{6}+\left(-40\right)\sqrt{2}\right)\left(\dfrac{41}{7}\right)\\
&=&\dfrac{2747}{42}+\left(-\dfrac{1640}{7}\right)\sqrt{2}\\
&=&\dfrac{2747}{42}+\left(-\dfrac{1640}{7}\right)\sqrt{2}\\
\end{eqnarray*}