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 \( X=-\dfrac{14}{3}-\dfrac{13}{8}-\left(\left(-8\right)\sqrt{175}+\left(-\dfrac{57}{4}\right)\sqrt{63}+\dfrac{71}{8}\right)\) et \( Y=\left(7\right)\sqrt{49}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(-\dfrac{14}{3}-\dfrac{13}{8}-\left(\left(-8\right)\sqrt{175}+\left(-\dfrac{57}{4}\right)\sqrt{63}+\dfrac{71}{8}\right)\right)+\left(\left(7\right)\sqrt{49}\right)\\
&=&\left(-\dfrac{14}{3}-\dfrac{13}{8}-\left(\left(-40\right)\sqrt{7}+\left(-\dfrac{171}{4}\right)\sqrt{7}+\dfrac{71}{8}\right)\right)+\left(49\right)\\
&=&-\dfrac{14}{3}-\dfrac{13}{8}-\left(\left(-40\right)\sqrt{7}+\left(-\dfrac{171}{4}\right)\sqrt{7}+\dfrac{71}{8}\right)+49\\
&=&\dfrac{203}{6}+\left(\dfrac{331}{4}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(-\dfrac{14}{3}-\dfrac{13}{8}-\left(\left(-8\right)\sqrt{175}+\left(-\dfrac{57}{4}\right)\sqrt{63}+\dfrac{71}{8}\right)\right)-\left(\left(7\right)\sqrt{49}\right)\\
&=&\left(-\dfrac{14}{3}-\dfrac{13}{8}-\left(\left(-40\right)\sqrt{7}+\left(-\dfrac{171}{4}\right)\sqrt{7}+\dfrac{71}{8}\right)\right)-\left(49\right)\\
&=&\left(-\dfrac{91}{6}+\left(\dfrac{331}{4}\right)\sqrt{7}\right)-\left(49\right)\\
&=&-\dfrac{91}{6}+\left(\dfrac{331}{4}\right)\sqrt{7}+-49\\
&=&-\dfrac{385}{6}+\left(\dfrac{331}{4}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(-\dfrac{14}{3}-\dfrac{13}{8}-\left(\left(-8\right)\sqrt{175}+\left(-\dfrac{57}{4}\right)\sqrt{63}+\dfrac{71}{8}\right)\right)\times\left(\left(7\right)\sqrt{49}\right)\\
&=&\left(-\dfrac{14}{3}-\dfrac{13}{8}-\left(\left(-40\right)\sqrt{7}+\left(-\dfrac{171}{4}\right)\sqrt{7}+\dfrac{71}{8}\right)\right)\times\left(49\right)\\
&=&\left(-\dfrac{91}{6}+\left(\dfrac{331}{4}\right)\sqrt{7}\right)\left(49\right)\\
&=&-\dfrac{4459}{6}+\left(\dfrac{16219}{4}\right)\sqrt{7}\\
&=&-\dfrac{4459}{6}+\left(\dfrac{16219}{4}\right)\sqrt{7}\\
\end{eqnarray*}