L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(-\dfrac{71}{6}\right)\sqrt{175}+\left(\dfrac{69}{2}\right)\sqrt{175}+\left(-\dfrac{3}{8}\right)\sqrt{63}+\dfrac{80}{3}+\left(0\right)\sqrt{28}\) et \( Y=\left(-\dfrac{65}{9}\right)\sqrt{63}\) . 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{71}{6}\right)\sqrt{175}+\left(\dfrac{69}{2}\right)\sqrt{175}+\left(-\dfrac{3}{8}\right)\sqrt{63}+\dfrac{80}{3}+\left(0\right)\sqrt{28}\right)+\left(\left(-\dfrac{65}{9}\right)\sqrt{63}\right)\\
&=&\left(\left(-\dfrac{355}{6}\right)\sqrt{7}+\left(\dfrac{345}{2}\right)\sqrt{7}+\left(-\dfrac{9}{8}\right)\sqrt{7}+\dfrac{80}{3}+\left(0\right)\sqrt{7}\right)+\left(\left(-\dfrac{65}{3}\right)\sqrt{7}\right)\\
&=&\left(-\dfrac{355}{6}\right)\sqrt{7}+\left(\dfrac{345}{2}\right)\sqrt{7}+\left(-\dfrac{9}{8}\right)\sqrt{7}+\dfrac{80}{3}+\left(0\right)\sqrt{7}+\left(-\dfrac{65}{3}\right)\sqrt{7}\\
&=&\left(\dfrac{2173}{24}\right)\sqrt{7}+\dfrac{80}{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{71}{6}\right)\sqrt{175}+\left(\dfrac{69}{2}\right)\sqrt{175}+\left(-\dfrac{3}{8}\right)\sqrt{63}+\dfrac{80}{3}+\left(0\right)\sqrt{28}\right)-\left(\left(-\dfrac{65}{9}\right)\sqrt{63}\right)\\
&=&\left(\left(-\dfrac{355}{6}\right)\sqrt{7}+\left(\dfrac{345}{2}\right)\sqrt{7}+\left(-\dfrac{9}{8}\right)\sqrt{7}+\dfrac{80}{3}+\left(0\right)\sqrt{7}\right)-\left(\left(-\dfrac{65}{3}\right)\sqrt{7}\right)\\
&=&\left(\left(\dfrac{2693}{24}\right)\sqrt{7}+\dfrac{80}{3}\right)-\left(\left(-\dfrac{65}{3}\right)\sqrt{7}\right)\\
&=&\left(\dfrac{2693}{24}\right)\sqrt{7}+\dfrac{80}{3}+\left(\dfrac{65}{3}\right)\sqrt{7}\\
&=&\left(\dfrac{1071}{8}\right)\sqrt{7}+\dfrac{80}{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{71}{6}\right)\sqrt{175}+\left(\dfrac{69}{2}\right)\sqrt{175}+\left(-\dfrac{3}{8}\right)\sqrt{63}+\dfrac{80}{3}+\left(0\right)\sqrt{28}\right)\times\left(\left(-\dfrac{65}{9}\right)\sqrt{63}\right)\\
&=&\left(\left(-\dfrac{355}{6}\right)\sqrt{7}+\left(\dfrac{345}{2}\right)\sqrt{7}+\left(-\dfrac{9}{8}\right)\sqrt{7}+\dfrac{80}{3}+\left(0\right)\sqrt{7}\right)\times\left(\left(-\dfrac{65}{3}\right)\sqrt{7}\right)\\
&=&\left(\left(\dfrac{2693}{24}\right)\sqrt{7}+\dfrac{80}{3}\right)\left(\left(-\dfrac{65}{3}\right)\sqrt{7}\right)\\
&=&\left(-\dfrac{175045}{72}\right)\sqrt{49}+\left(-\dfrac{5200}{9}\right)\sqrt{7}\\
&=&-\dfrac{1225315}{72}+\left(-\dfrac{5200}{9}\right)\sqrt{7}\\
\end{eqnarray*}