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 \( X=\left(\dfrac{12}{7}\right)\sqrt{9}\) et \( Y=\left(-\dfrac{67}{9}-\left(\left(4\right)\sqrt{27}\right)-\dfrac{10}{3}\right)-\left(\left(\dfrac{57}{4}\right)\sqrt{27}+\left(-\dfrac{19}{6}\right)\sqrt{9}\right)\) . 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{12}{7}\right)\sqrt{9}\right)+\left(\left(-\dfrac{67}{9}-\left(\left(4\right)\sqrt{27}\right)-\dfrac{10}{3}\right)-\left(\left(\dfrac{57}{4}\right)\sqrt{27}+\left(-\dfrac{19}{6}\right)\sqrt{9}\right)\right)\\
&=&\left(\dfrac{36}{7}\right)+\left(\left(-\dfrac{67}{9}-\left(\left(12\right)\sqrt{3}\right)-\dfrac{10}{3}\right)-\left(\left(\dfrac{171}{4}\right)\sqrt{3}-\dfrac{19}{2}\right)\right)\\
&=&\dfrac{36}{7}+\left(-\dfrac{67}{9}-\left(\left(12\right)\sqrt{3}\right)-\dfrac{10}{3}\right)-\left(\left(\dfrac{171}{4}\right)\sqrt{3}-\dfrac{19}{2}\right)\\
&=&\dfrac{487}{126}+\left(-\dfrac{219}{4}\right)\sqrt{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\dfrac{12}{7}\right)\sqrt{9}\right)-\left(\left(-\dfrac{67}{9}-\left(\left(4\right)\sqrt{27}\right)-\dfrac{10}{3}\right)-\left(\left(\dfrac{57}{4}\right)\sqrt{27}+\left(-\dfrac{19}{6}\right)\sqrt{9}\right)\right)\\
&=&\left(\dfrac{36}{7}\right)-\left(\left(-\dfrac{67}{9}-\left(\left(12\right)\sqrt{3}\right)-\dfrac{10}{3}\right)-\left(\left(\dfrac{171}{4}\right)\sqrt{3}-\dfrac{19}{2}\right)\right)\\
&=&\left(\dfrac{36}{7}\right)-\left(-\dfrac{23}{18}+\left(-\dfrac{219}{4}\right)\sqrt{3}\right)\\
&=&\dfrac{36}{7}+\dfrac{23}{18}+\left(\dfrac{219}{4}\right)\sqrt{3}\\
&=&\dfrac{809}{126}+\left(\dfrac{219}{4}\right)\sqrt{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\dfrac{12}{7}\right)\sqrt{9}\right)\times\left(\left(-\dfrac{67}{9}-\left(\left(4\right)\sqrt{27}\right)-\dfrac{10}{3}\right)-\left(\left(\dfrac{57}{4}\right)\sqrt{27}+\left(-\dfrac{19}{6}\right)\sqrt{9}\right)\right)\\
&=&\left(\dfrac{36}{7}\right)\times\left(\left(-\dfrac{67}{9}-\left(\left(12\right)\sqrt{3}\right)-\dfrac{10}{3}\right)-\left(\left(\dfrac{171}{4}\right)\sqrt{3}-\dfrac{19}{2}\right)\right)\\
&=&\left(\dfrac{36}{7}\right)\left(-\dfrac{23}{18}+\left(-\dfrac{219}{4}\right)\sqrt{3}\right)\\
&=&-\dfrac{46}{7}+\left(-\dfrac{1971}{7}\right)\sqrt{3}\\
&=&-\dfrac{46}{7}+\left(-\dfrac{1971}{7}\right)\sqrt{3}\\
\end{eqnarray*}