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 \( X=\left(\left(\dfrac{55}{7}\right)\sqrt{27}\right)-\left(\left(-\dfrac{9}{4}\right)\sqrt{12}\right)+\left(\left(-\dfrac{30}{7}\right)\sqrt{9}\right)-\left(\left(8\right)\sqrt{12}\right)-\left(\left(\dfrac{55}{7}\right)\sqrt{27}\right)-\left(\left(-\dfrac{3}{4}\right)\sqrt{12}\right)-9+\left(\dfrac{67}{4}\right)\sqrt{27}\) et \( Y=\left(-\dfrac{57}{7}\right)\sqrt{75}\) . 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(\dfrac{55}{7}\right)\sqrt{27}\right)-\left(\left(-\dfrac{9}{4}\right)\sqrt{12}\right)+\left(\left(-\dfrac{30}{7}\right)\sqrt{9}\right)-\left(\left(8\right)\sqrt{12}\right)-\left(\left(\dfrac{55}{7}\right)\sqrt{27}\right)-\left(\left(-\dfrac{3}{4}\right)\sqrt{12}\right)-9+\left(\dfrac{67}{4}\right)\sqrt{27}\right)+\left(\left(-\dfrac{57}{7}\right)\sqrt{75}\right)\\
&=&\left(\left(\left(\dfrac{165}{7}\right)\sqrt{3}\right)-\left(\left(-\dfrac{9}{2}\right)\sqrt{3}\right)-\dfrac{90}{7}-\left(\left(16\right)\sqrt{3}\right)-\left(\left(\dfrac{165}{7}\right)\sqrt{3}\right)-\left(\left(-\dfrac{3}{2}\right)\sqrt{3}\right)-9+\left(\dfrac{201}{4}\right)\sqrt{3}\right)+\left(\left(-\dfrac{285}{7}\right)\sqrt{3}\right)\\
&=&\left(\left(\dfrac{165}{7}\right)\sqrt{3}\right)-\left(\left(-\dfrac{9}{2}\right)\sqrt{3}\right)-\dfrac{90}{7}-\left(\left(16\right)\sqrt{3}\right)-\left(\left(\dfrac{165}{7}\right)\sqrt{3}\right)-\left(\left(-\dfrac{3}{2}\right)\sqrt{3}\right)-9+\left(\dfrac{201}{4}\right)\sqrt{3}+\left(-\dfrac{285}{7}\right)\sqrt{3}\\
&=&\left(-\dfrac{13}{28}\right)\sqrt{3}-\dfrac{153}{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(\dfrac{55}{7}\right)\sqrt{27}\right)-\left(\left(-\dfrac{9}{4}\right)\sqrt{12}\right)+\left(\left(-\dfrac{30}{7}\right)\sqrt{9}\right)-\left(\left(8\right)\sqrt{12}\right)-\left(\left(\dfrac{55}{7}\right)\sqrt{27}\right)-\left(\left(-\dfrac{3}{4}\right)\sqrt{12}\right)-9+\left(\dfrac{67}{4}\right)\sqrt{27}\right)-\left(\left(-\dfrac{57}{7}\right)\sqrt{75}\right)\\
&=&\left(\left(\left(\dfrac{165}{7}\right)\sqrt{3}\right)-\left(\left(-\dfrac{9}{2}\right)\sqrt{3}\right)-\dfrac{90}{7}-\left(\left(16\right)\sqrt{3}\right)-\left(\left(\dfrac{165}{7}\right)\sqrt{3}\right)-\left(\left(-\dfrac{3}{2}\right)\sqrt{3}\right)-9+\left(\dfrac{201}{4}\right)\sqrt{3}\right)-\left(\left(-\dfrac{285}{7}\right)\sqrt{3}\right)\\
&=&\left(\left(\dfrac{161}{4}\right)\sqrt{3}-\dfrac{153}{7}\right)-\left(\left(-\dfrac{285}{7}\right)\sqrt{3}\right)\\
&=&\left(\dfrac{161}{4}\right)\sqrt{3}-\dfrac{153}{7}+\left(\dfrac{285}{7}\right)\sqrt{3}\\
&=&\left(\dfrac{2267}{28}\right)\sqrt{3}-\dfrac{153}{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(\dfrac{55}{7}\right)\sqrt{27}\right)-\left(\left(-\dfrac{9}{4}\right)\sqrt{12}\right)+\left(\left(-\dfrac{30}{7}\right)\sqrt{9}\right)-\left(\left(8\right)\sqrt{12}\right)-\left(\left(\dfrac{55}{7}\right)\sqrt{27}\right)-\left(\left(-\dfrac{3}{4}\right)\sqrt{12}\right)-9+\left(\dfrac{67}{4}\right)\sqrt{27}\right)\times\left(\left(-\dfrac{57}{7}\right)\sqrt{75}\right)\\
&=&\left(\left(\left(\dfrac{165}{7}\right)\sqrt{3}\right)-\left(\left(-\dfrac{9}{2}\right)\sqrt{3}\right)-\dfrac{90}{7}-\left(\left(16\right)\sqrt{3}\right)-\left(\left(\dfrac{165}{7}\right)\sqrt{3}\right)-\left(\left(-\dfrac{3}{2}\right)\sqrt{3}\right)-9+\left(\dfrac{201}{4}\right)\sqrt{3}\right)\times\left(\left(-\dfrac{285}{7}\right)\sqrt{3}\right)\\
&=&\left(\left(\dfrac{161}{4}\right)\sqrt{3}-\dfrac{153}{7}\right)\left(\left(-\dfrac{285}{7}\right)\sqrt{3}\right)\\
&=&\left(-\dfrac{6555}{4}\right)\sqrt{9}+\left(\dfrac{43605}{49}\right)\sqrt{3}\\
&=&-\dfrac{19665}{4}+\left(\dfrac{43605}{49}\right)\sqrt{3}\\
\end{eqnarray*}