L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(-\dfrac{29}{9}\right)\sqrt{18}\) et \( Y=\left(\left(6\right)\sqrt{18}\right)-\left(\left(-\dfrac{29}{4}\right)\sqrt{50}\right)+\dfrac{8}{7}-\dfrac{42}{5}+\left(1\right)\sqrt{50}\) . 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{29}{9}\right)\sqrt{18}\right)+\left(\left(\left(6\right)\sqrt{18}\right)-\left(\left(-\dfrac{29}{4}\right)\sqrt{50}\right)+\dfrac{8}{7}-\dfrac{42}{5}+\left(1\right)\sqrt{50}\right)\\
&=&\left(\left(-\dfrac{29}{3}\right)\sqrt{2}\right)+\left(\left(\left(18\right)\sqrt{2}\right)-\left(\left(-\dfrac{145}{4}\right)\sqrt{2}\right)+\dfrac{8}{7}-\dfrac{42}{5}+\left(5\right)\sqrt{2}\right)\\
&=&\left(-\dfrac{29}{3}\right)\sqrt{2}+\left(\left(18\right)\sqrt{2}\right)-\left(\left(-\dfrac{145}{4}\right)\sqrt{2}\right)+\dfrac{8}{7}-\dfrac{42}{5}+\left(5\right)\sqrt{2}\\
&=&\left(\dfrac{595}{12}\right)\sqrt{2}-\dfrac{254}{35}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{29}{9}\right)\sqrt{18}\right)-\left(\left(\left(6\right)\sqrt{18}\right)-\left(\left(-\dfrac{29}{4}\right)\sqrt{50}\right)+\dfrac{8}{7}-\dfrac{42}{5}+\left(1\right)\sqrt{50}\right)\\
&=&\left(\left(-\dfrac{29}{3}\right)\sqrt{2}\right)-\left(\left(\left(18\right)\sqrt{2}\right)-\left(\left(-\dfrac{145}{4}\right)\sqrt{2}\right)+\dfrac{8}{7}-\dfrac{42}{5}+\left(5\right)\sqrt{2}\right)\\
&=&\left(\left(-\dfrac{29}{3}\right)\sqrt{2}\right)-\left(\left(\dfrac{237}{4}\right)\sqrt{2}-\dfrac{254}{35}\right)\\
&=&\left(-\dfrac{29}{3}\right)\sqrt{2}+\left(-\dfrac{237}{4}\right)\sqrt{2}+\dfrac{254}{35}\\
&=&\left(-\dfrac{827}{12}\right)\sqrt{2}+\dfrac{254}{35}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{29}{9}\right)\sqrt{18}\right)\times\left(\left(\left(6\right)\sqrt{18}\right)-\left(\left(-\dfrac{29}{4}\right)\sqrt{50}\right)+\dfrac{8}{7}-\dfrac{42}{5}+\left(1\right)\sqrt{50}\right)\\
&=&\left(\left(-\dfrac{29}{3}\right)\sqrt{2}\right)\times\left(\left(\left(18\right)\sqrt{2}\right)-\left(\left(-\dfrac{145}{4}\right)\sqrt{2}\right)+\dfrac{8}{7}-\dfrac{42}{5}+\left(5\right)\sqrt{2}\right)\\
&=&\left(\left(-\dfrac{29}{3}\right)\sqrt{2}\right)\left(\left(\dfrac{237}{4}\right)\sqrt{2}-\dfrac{254}{35}\right)\\
&=&\left(-\dfrac{2291}{4}\right)\sqrt{4}+\left(\dfrac{7366}{105}\right)\sqrt{2}\\
&=&-\dfrac{2291}{2}+\left(\dfrac{7366}{105}\right)\sqrt{2}\\
\end{eqnarray*}