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 \( X=\left(\left(\left(-\dfrac{81}{5}\right)\sqrt{20}\right)-\left(\left(-\dfrac{14}{9}\right)\sqrt{125}\right)\right)-\left(\left(-\dfrac{22}{3}\right)\sqrt{125}+\left(-\dfrac{9}{5}\right)\sqrt{20}\right)\) et \( Y=-\dfrac{38}{7}\) . 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(\left(-\dfrac{81}{5}\right)\sqrt{20}\right)-\left(\left(-\dfrac{14}{9}\right)\sqrt{125}\right)\right)-\left(\left(-\dfrac{22}{3}\right)\sqrt{125}+\left(-\dfrac{9}{5}\right)\sqrt{20}\right)\right)+\left(-\dfrac{38}{7}\right)\\
&=&\left(\left(\left(\left(-\dfrac{162}{5}\right)\sqrt{5}\right)-\left(\left(-\dfrac{70}{9}\right)\sqrt{5}\right)\right)-\left(\left(-\dfrac{110}{3}\right)\sqrt{5}+\left(-\dfrac{18}{5}\right)\sqrt{5}\right)\right)+\left(-\dfrac{38}{7}\right)\\
&=&\left(\left(\left(-\dfrac{162}{5}\right)\sqrt{5}\right)-\left(\left(-\dfrac{70}{9}\right)\sqrt{5}\right)\right)-\left(\left(-\dfrac{110}{3}\right)\sqrt{5}+\left(-\dfrac{18}{5}\right)\sqrt{5}\right)-\dfrac{38}{7}\\
&=&\left(\dfrac{704}{45}\right)\sqrt{5}-\dfrac{38}{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(\left(-\dfrac{81}{5}\right)\sqrt{20}\right)-\left(\left(-\dfrac{14}{9}\right)\sqrt{125}\right)\right)-\left(\left(-\dfrac{22}{3}\right)\sqrt{125}+\left(-\dfrac{9}{5}\right)\sqrt{20}\right)\right)-\left(-\dfrac{38}{7}\right)\\
&=&\left(\left(\left(\left(-\dfrac{162}{5}\right)\sqrt{5}\right)-\left(\left(-\dfrac{70}{9}\right)\sqrt{5}\right)\right)-\left(\left(-\dfrac{110}{3}\right)\sqrt{5}+\left(-\dfrac{18}{5}\right)\sqrt{5}\right)\right)-\left(-\dfrac{38}{7}\right)\\
&=&\left(\left(\dfrac{704}{45}\right)\sqrt{5}\right)-\left(-\dfrac{38}{7}\right)\\
&=&\left(\dfrac{704}{45}\right)\sqrt{5}+\dfrac{38}{7}\\
&=&\left(\dfrac{704}{45}\right)\sqrt{5}+\dfrac{38}{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(\left(-\dfrac{81}{5}\right)\sqrt{20}\right)-\left(\left(-\dfrac{14}{9}\right)\sqrt{125}\right)\right)-\left(\left(-\dfrac{22}{3}\right)\sqrt{125}+\left(-\dfrac{9}{5}\right)\sqrt{20}\right)\right)\times\left(-\dfrac{38}{7}\right)\\
&=&\left(\left(\left(\left(-\dfrac{162}{5}\right)\sqrt{5}\right)-\left(\left(-\dfrac{70}{9}\right)\sqrt{5}\right)\right)-\left(\left(-\dfrac{110}{3}\right)\sqrt{5}+\left(-\dfrac{18}{5}\right)\sqrt{5}\right)\right)\times\left(-\dfrac{38}{7}\right)\\
&=&\left(\left(\dfrac{704}{45}\right)\sqrt{5}\right)\left(-\dfrac{38}{7}\right)\\
&=&\left(-\dfrac{26752}{315}\right)\sqrt{5}\\
&=&\left(-\dfrac{26752}{315}\right)\sqrt{5}\\
\end{eqnarray*}