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 \( X=\left(\dfrac{81}{5}\right)\sqrt{175}-6-\left(\left(-1\right)\sqrt{49}\right)-\dfrac{68}{3}-\left(\left(-\dfrac{13}{2}\right)\sqrt{28}\right)+\left(\left(-\dfrac{49}{5}\right)\sqrt{28}\right)-\left(\left(-\dfrac{53}{5}\right)\sqrt{175}\right)-\left(\left(-\dfrac{31}{3}\right)\sqrt{28}\right)+\left(6\right)\sqrt{63}\) et \( Y=\left(\dfrac{19}{4}\right)\sqrt{49}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(\dfrac{81}{5}\right)\sqrt{175}-6-\left(\left(-1\right)\sqrt{49}\right)-\dfrac{68}{3}-\left(\left(-\dfrac{13}{2}\right)\sqrt{28}\right)+\left(\left(-\dfrac{49}{5}\right)\sqrt{28}\right)-\left(\left(-\dfrac{53}{5}\right)\sqrt{175}\right)-\left(\left(-\dfrac{31}{3}\right)\sqrt{28}\right)+\left(6\right)\sqrt{63}\right)+\left(\left(\dfrac{19}{4}\right)\sqrt{49}\right)\\
&=&\left(\left(81\right)\sqrt{7}-6+7-\dfrac{68}{3}-\left(\left(-13\right)\sqrt{7}\right)+\left(\left(-\dfrac{98}{5}\right)\sqrt{7}\right)-\left(\left(-53\right)\sqrt{7}\right)-\left(\left(-\dfrac{62}{3}\right)\sqrt{7}\right)+\left(18\right)\sqrt{7}\right)+\left(\dfrac{133}{4}\right)\\
&=&\left(81\right)\sqrt{7}-6+7-\dfrac{68}{3}-\left(\left(-13\right)\sqrt{7}\right)+\left(\left(-\dfrac{98}{5}\right)\sqrt{7}\right)-\left(\left(-53\right)\sqrt{7}\right)-\left(\left(-\dfrac{62}{3}\right)\sqrt{7}\right)+\left(18\right)\sqrt{7}+\dfrac{133}{4}\\
&=&\left(\dfrac{2491}{15}\right)\sqrt{7}+\dfrac{139}{12}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\dfrac{81}{5}\right)\sqrt{175}-6-\left(\left(-1\right)\sqrt{49}\right)-\dfrac{68}{3}-\left(\left(-\dfrac{13}{2}\right)\sqrt{28}\right)+\left(\left(-\dfrac{49}{5}\right)\sqrt{28}\right)-\left(\left(-\dfrac{53}{5}\right)\sqrt{175}\right)-\left(\left(-\dfrac{31}{3}\right)\sqrt{28}\right)+\left(6\right)\sqrt{63}\right)-\left(\left(\dfrac{19}{4}\right)\sqrt{49}\right)\\
&=&\left(\left(81\right)\sqrt{7}-6+7-\dfrac{68}{3}-\left(\left(-13\right)\sqrt{7}\right)+\left(\left(-\dfrac{98}{5}\right)\sqrt{7}\right)-\left(\left(-53\right)\sqrt{7}\right)-\left(\left(-\dfrac{62}{3}\right)\sqrt{7}\right)+\left(18\right)\sqrt{7}\right)-\left(\dfrac{133}{4}\right)\\
&=&\left(\left(\dfrac{2491}{15}\right)\sqrt{7}-\dfrac{65}{3}\right)-\left(\dfrac{133}{4}\right)\\
&=&\left(\dfrac{2491}{15}\right)\sqrt{7}-\dfrac{65}{3}+-\dfrac{133}{4}\\
&=&\left(\dfrac{2491}{15}\right)\sqrt{7}-\dfrac{659}{12}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\dfrac{81}{5}\right)\sqrt{175}-6-\left(\left(-1\right)\sqrt{49}\right)-\dfrac{68}{3}-\left(\left(-\dfrac{13}{2}\right)\sqrt{28}\right)+\left(\left(-\dfrac{49}{5}\right)\sqrt{28}\right)-\left(\left(-\dfrac{53}{5}\right)\sqrt{175}\right)-\left(\left(-\dfrac{31}{3}\right)\sqrt{28}\right)+\left(6\right)\sqrt{63}\right)\times\left(\left(\dfrac{19}{4}\right)\sqrt{49}\right)\\
&=&\left(\left(81\right)\sqrt{7}-6+7-\dfrac{68}{3}-\left(\left(-13\right)\sqrt{7}\right)+\left(\left(-\dfrac{98}{5}\right)\sqrt{7}\right)-\left(\left(-53\right)\sqrt{7}\right)-\left(\left(-\dfrac{62}{3}\right)\sqrt{7}\right)+\left(18\right)\sqrt{7}\right)\times\left(\dfrac{133}{4}\right)\\
&=&\left(\left(\dfrac{2491}{15}\right)\sqrt{7}-\dfrac{65}{3}\right)\left(\dfrac{133}{4}\right)\\
&=&\left(\dfrac{331303}{60}\right)\sqrt{7}-\dfrac{8645}{12}\\
&=&\left(\dfrac{331303}{60}\right)\sqrt{7}-\dfrac{8645}{12}\\
\end{eqnarray*}