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 \( X=\left(\left(\dfrac{75}{8}\right)\sqrt{18}\right)-\left(\left(-\dfrac{79}{4}\right)\sqrt{4}\right)-\left(\left(\left(\dfrac{72}{7}\right)\sqrt{8}\right)+\dfrac{50}{3}\right)-\left(-\dfrac{27}{2}-\left(\left(\dfrac{18}{7}\right)\sqrt{4}\right)-\left(\left(-9\right)\sqrt{8}\right)\right)\) et \( Y=\left(\dfrac{41}{5}\right)\sqrt{8}\) . 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{75}{8}\right)\sqrt{18}\right)-\left(\left(-\dfrac{79}{4}\right)\sqrt{4}\right)-\left(\left(\left(\dfrac{72}{7}\right)\sqrt{8}\right)+\dfrac{50}{3}\right)-\left(-\dfrac{27}{2}-\left(\left(\dfrac{18}{7}\right)\sqrt{4}\right)-\left(\left(-9\right)\sqrt{8}\right)\right)\right)+\left(\left(\dfrac{41}{5}\right)\sqrt{8}\right)\\
&=&\left(\left(\left(\dfrac{225}{8}\right)\sqrt{2}\right)+\dfrac{79}{2}-\left(\left(\left(\dfrac{144}{7}\right)\sqrt{2}\right)+\dfrac{50}{3}\right)-\left(-\dfrac{27}{2}-\dfrac{36}{7}-\left(\left(-18\right)\sqrt{2}\right)\right)\right)+\left(\left(\dfrac{82}{5}\right)\sqrt{2}\right)\\
&=&\left(\left(\dfrac{225}{8}\right)\sqrt{2}\right)+\dfrac{79}{2}-\left(\left(\left(\dfrac{144}{7}\right)\sqrt{2}\right)+\dfrac{50}{3}\right)-\left(-\dfrac{27}{2}-\dfrac{36}{7}-\left(\left(-18\right)\sqrt{2}\right)\right)+\left(\dfrac{82}{5}\right)\sqrt{2}\\
&=&\left(\dfrac{1667}{280}\right)\sqrt{2}+\dfrac{871}{21}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(\dfrac{75}{8}\right)\sqrt{18}\right)-\left(\left(-\dfrac{79}{4}\right)\sqrt{4}\right)-\left(\left(\left(\dfrac{72}{7}\right)\sqrt{8}\right)+\dfrac{50}{3}\right)-\left(-\dfrac{27}{2}-\left(\left(\dfrac{18}{7}\right)\sqrt{4}\right)-\left(\left(-9\right)\sqrt{8}\right)\right)\right)-\left(\left(\dfrac{41}{5}\right)\sqrt{8}\right)\\
&=&\left(\left(\left(\dfrac{225}{8}\right)\sqrt{2}\right)+\dfrac{79}{2}-\left(\left(\left(\dfrac{144}{7}\right)\sqrt{2}\right)+\dfrac{50}{3}\right)-\left(-\dfrac{27}{2}-\dfrac{36}{7}-\left(\left(-18\right)\sqrt{2}\right)\right)\right)-\left(\left(\dfrac{82}{5}\right)\sqrt{2}\right)\\
&=&\left(\left(-\dfrac{585}{56}\right)\sqrt{2}+\dfrac{871}{21}\right)-\left(\left(\dfrac{82}{5}\right)\sqrt{2}\right)\\
&=&\left(-\dfrac{585}{56}\right)\sqrt{2}+\dfrac{871}{21}+\left(-\dfrac{82}{5}\right)\sqrt{2}\\
&=&\left(-\dfrac{7517}{280}\right)\sqrt{2}+\dfrac{871}{21}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(\dfrac{75}{8}\right)\sqrt{18}\right)-\left(\left(-\dfrac{79}{4}\right)\sqrt{4}\right)-\left(\left(\left(\dfrac{72}{7}\right)\sqrt{8}\right)+\dfrac{50}{3}\right)-\left(-\dfrac{27}{2}-\left(\left(\dfrac{18}{7}\right)\sqrt{4}\right)-\left(\left(-9\right)\sqrt{8}\right)\right)\right)\times\left(\left(\dfrac{41}{5}\right)\sqrt{8}\right)\\
&=&\left(\left(\left(\dfrac{225}{8}\right)\sqrt{2}\right)+\dfrac{79}{2}-\left(\left(\left(\dfrac{144}{7}\right)\sqrt{2}\right)+\dfrac{50}{3}\right)-\left(-\dfrac{27}{2}-\dfrac{36}{7}-\left(\left(-18\right)\sqrt{2}\right)\right)\right)\times\left(\left(\dfrac{82}{5}\right)\sqrt{2}\right)\\
&=&\left(\left(-\dfrac{585}{56}\right)\sqrt{2}+\dfrac{871}{21}\right)\left(\left(\dfrac{82}{5}\right)\sqrt{2}\right)\\
&=&\left(-\dfrac{4797}{28}\right)\sqrt{4}+\left(\dfrac{71422}{105}\right)\sqrt{2}\\
&=&-\dfrac{4797}{14}+\left(\dfrac{71422}{105}\right)\sqrt{2}\\
\end{eqnarray*}