L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(-9\right)\sqrt{63}\) et \( Y=\left(\dfrac{44}{9}\right)\sqrt{63}+\left(-\dfrac{33}{4}\right)\sqrt{175}+\left(\dfrac{3}{7}\right)\sqrt{49}+\left(\dfrac{34}{9}\right)\sqrt{175}+\left(\dfrac{67}{4}\right)\sqrt{175}+\left(\dfrac{9}{5}\right)\sqrt{175}+\left(0\right)\sqrt{49}+\left(9\right)\sqrt{63}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(-9\right)\sqrt{63}\right)+\left(\left(\dfrac{44}{9}\right)\sqrt{63}+\left(-\dfrac{33}{4}\right)\sqrt{175}+\left(\dfrac{3}{7}\right)\sqrt{49}+\left(\dfrac{34}{9}\right)\sqrt{175}+\left(\dfrac{67}{4}\right)\sqrt{175}+\left(\dfrac{9}{5}\right)\sqrt{175}+\left(0\right)\sqrt{49}+\left(9\right)\sqrt{63}\right)\\
&=&\left(\left(-27\right)\sqrt{7}\right)+\left(\left(\dfrac{44}{3}\right)\sqrt{7}+\left(-\dfrac{165}{4}\right)\sqrt{7}+3+\left(\dfrac{170}{9}\right)\sqrt{7}+\left(\dfrac{335}{4}\right)\sqrt{7}+\left(9\right)\sqrt{7}+0+\left(27\right)\sqrt{7}\right)\\
&=&\left(-27\right)\sqrt{7}+\left(\dfrac{44}{3}\right)\sqrt{7}+\left(-\dfrac{165}{4}\right)\sqrt{7}+3+\left(\dfrac{170}{9}\right)\sqrt{7}+\left(\dfrac{335}{4}\right)\sqrt{7}+\left(9\right)\sqrt{7}+0+\left(27\right)\sqrt{7}\\
&=&\left(\dfrac{1531}{18}\right)\sqrt{7}+3\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-9\right)\sqrt{63}\right)-\left(\left(\dfrac{44}{9}\right)\sqrt{63}+\left(-\dfrac{33}{4}\right)\sqrt{175}+\left(\dfrac{3}{7}\right)\sqrt{49}+\left(\dfrac{34}{9}\right)\sqrt{175}+\left(\dfrac{67}{4}\right)\sqrt{175}+\left(\dfrac{9}{5}\right)\sqrt{175}+\left(0\right)\sqrt{49}+\left(9\right)\sqrt{63}\right)\\
&=&\left(\left(-27\right)\sqrt{7}\right)-\left(\left(\dfrac{44}{3}\right)\sqrt{7}+\left(-\dfrac{165}{4}\right)\sqrt{7}+3+\left(\dfrac{170}{9}\right)\sqrt{7}+\left(\dfrac{335}{4}\right)\sqrt{7}+\left(9\right)\sqrt{7}+0+\left(27\right)\sqrt{7}\right)\\
&=&\left(\left(-27\right)\sqrt{7}\right)-\left(\left(\dfrac{2017}{18}\right)\sqrt{7}+3\right)\\
&=&\left(-27\right)\sqrt{7}+\left(-\dfrac{2017}{18}\right)\sqrt{7}-3\\
&=&\left(-\dfrac{2503}{18}\right)\sqrt{7}-3\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-9\right)\sqrt{63}\right)\times\left(\left(\dfrac{44}{9}\right)\sqrt{63}+\left(-\dfrac{33}{4}\right)\sqrt{175}+\left(\dfrac{3}{7}\right)\sqrt{49}+\left(\dfrac{34}{9}\right)\sqrt{175}+\left(\dfrac{67}{4}\right)\sqrt{175}+\left(\dfrac{9}{5}\right)\sqrt{175}+\left(0\right)\sqrt{49}+\left(9\right)\sqrt{63}\right)\\
&=&\left(\left(-27\right)\sqrt{7}\right)\times\left(\left(\dfrac{44}{3}\right)\sqrt{7}+\left(-\dfrac{165}{4}\right)\sqrt{7}+3+\left(\dfrac{170}{9}\right)\sqrt{7}+\left(\dfrac{335}{4}\right)\sqrt{7}+\left(9\right)\sqrt{7}+0+\left(27\right)\sqrt{7}\right)\\
&=&\left(\left(-27\right)\sqrt{7}\right)\left(\left(\dfrac{2017}{18}\right)\sqrt{7}+3\right)\\
&=&\left(-\dfrac{6051}{2}\right)\sqrt{49}+\left(-81\right)\sqrt{7}\\
&=&-\dfrac{42357}{2}+\left(-81\right)\sqrt{7}\\
\end{eqnarray*}