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 \( X=\left(\left(0\right)\sqrt{27}\right)-\left(\left(0\right)\sqrt{27}\right)+\left(\dfrac{75}{8}\right)\sqrt{27}+\dfrac{62}{5}\) et \( Y=\left(3\right)\sqrt{9}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(\left(0\right)\sqrt{27}\right)-\left(\left(0\right)\sqrt{27}\right)+\left(\dfrac{75}{8}\right)\sqrt{27}+\dfrac{62}{5}\right)+\left(\left(3\right)\sqrt{9}\right)\\
&=&\left(\left(\left(0\right)\sqrt{3}\right)-\left(\left(0\right)\sqrt{3}\right)+\left(\dfrac{225}{8}\right)\sqrt{3}+\dfrac{62}{5}\right)+\left(9\right)\\
&=&\left(\left(0\right)\sqrt{3}\right)-\left(\left(0\right)\sqrt{3}\right)+\left(\dfrac{225}{8}\right)\sqrt{3}+\dfrac{62}{5}+9\\
&=&\left(\dfrac{225}{8}\right)\sqrt{3}+\dfrac{107}{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(0\right)\sqrt{27}\right)-\left(\left(0\right)\sqrt{27}\right)+\left(\dfrac{75}{8}\right)\sqrt{27}+\dfrac{62}{5}\right)-\left(\left(3\right)\sqrt{9}\right)\\
&=&\left(\left(\left(0\right)\sqrt{3}\right)-\left(\left(0\right)\sqrt{3}\right)+\left(\dfrac{225}{8}\right)\sqrt{3}+\dfrac{62}{5}\right)-\left(9\right)\\
&=&\left(\left(\dfrac{225}{8}\right)\sqrt{3}+\dfrac{62}{5}\right)-\left(9\right)\\
&=&\left(\dfrac{225}{8}\right)\sqrt{3}+\dfrac{62}{5}+-9\\
&=&\left(\dfrac{225}{8}\right)\sqrt{3}+\dfrac{17}{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(0\right)\sqrt{27}\right)-\left(\left(0\right)\sqrt{27}\right)+\left(\dfrac{75}{8}\right)\sqrt{27}+\dfrac{62}{5}\right)\times\left(\left(3\right)\sqrt{9}\right)\\
&=&\left(\left(\left(0\right)\sqrt{3}\right)-\left(\left(0\right)\sqrt{3}\right)+\left(\dfrac{225}{8}\right)\sqrt{3}+\dfrac{62}{5}\right)\times\left(9\right)\\
&=&\left(\left(\dfrac{225}{8}\right)\sqrt{3}+\dfrac{62}{5}\right)\left(9\right)\\
&=&\left(\dfrac{2025}{8}\right)\sqrt{3}+\dfrac{558}{5}\\
&=&\left(\dfrac{2025}{8}\right)\sqrt{3}+\dfrac{558}{5}\\
\end{eqnarray*}