L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(-9\right)\sqrt{8}\) et \( Y=\dfrac{21}{4}+3-\left(\left(-\dfrac{9}{2}\right)\sqrt{50}\right)+\left(3\right)\sqrt{8}+\left(\dfrac{77}{3}\right)\sqrt{50}+\left(-\dfrac{28}{5}\right)\sqrt{4}+\left(-\dfrac{17}{2}\right)\sqrt{4}+\left(\dfrac{76}{9}\right)\sqrt{4}\) . 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{8}\right)+\left(\dfrac{21}{4}+3-\left(\left(-\dfrac{9}{2}\right)\sqrt{50}\right)+\left(3\right)\sqrt{8}+\left(\dfrac{77}{3}\right)\sqrt{50}+\left(-\dfrac{28}{5}\right)\sqrt{4}+\left(-\dfrac{17}{2}\right)\sqrt{4}+\left(\dfrac{76}{9}\right)\sqrt{4}\right)\\
&=&\left(\left(-18\right)\sqrt{2}\right)+\left(\dfrac{21}{4}+3-\left(\left(-\dfrac{45}{2}\right)\sqrt{2}\right)+\left(6\right)\sqrt{2}+\left(\dfrac{385}{3}\right)\sqrt{2}-\dfrac{56}{5}-17+\dfrac{152}{9}\right)\\
&=&\left(-18\right)\sqrt{2}+\dfrac{21}{4}+3-\left(\left(-\dfrac{45}{2}\right)\sqrt{2}\right)+\left(6\right)\sqrt{2}+\left(\dfrac{385}{3}\right)\sqrt{2}-\dfrac{56}{5}-17+\dfrac{152}{9}\\
&=&\left(\dfrac{833}{6}\right)\sqrt{2}-\dfrac{551}{180}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-9\right)\sqrt{8}\right)-\left(\dfrac{21}{4}+3-\left(\left(-\dfrac{9}{2}\right)\sqrt{50}\right)+\left(3\right)\sqrt{8}+\left(\dfrac{77}{3}\right)\sqrt{50}+\left(-\dfrac{28}{5}\right)\sqrt{4}+\left(-\dfrac{17}{2}\right)\sqrt{4}+\left(\dfrac{76}{9}\right)\sqrt{4}\right)\\
&=&\left(\left(-18\right)\sqrt{2}\right)-\left(\dfrac{21}{4}+3-\left(\left(-\dfrac{45}{2}\right)\sqrt{2}\right)+\left(6\right)\sqrt{2}+\left(\dfrac{385}{3}\right)\sqrt{2}-\dfrac{56}{5}-17+\dfrac{152}{9}\right)\\
&=&\left(\left(-18\right)\sqrt{2}\right)-\left(-\dfrac{551}{180}+\left(\dfrac{941}{6}\right)\sqrt{2}\right)\\
&=&\left(-18\right)\sqrt{2}+\dfrac{551}{180}+\left(-\dfrac{941}{6}\right)\sqrt{2}\\
&=&\left(-\dfrac{1049}{6}\right)\sqrt{2}+\dfrac{551}{180}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-9\right)\sqrt{8}\right)\times\left(\dfrac{21}{4}+3-\left(\left(-\dfrac{9}{2}\right)\sqrt{50}\right)+\left(3\right)\sqrt{8}+\left(\dfrac{77}{3}\right)\sqrt{50}+\left(-\dfrac{28}{5}\right)\sqrt{4}+\left(-\dfrac{17}{2}\right)\sqrt{4}+\left(\dfrac{76}{9}\right)\sqrt{4}\right)\\
&=&\left(\left(-18\right)\sqrt{2}\right)\times\left(\dfrac{21}{4}+3-\left(\left(-\dfrac{45}{2}\right)\sqrt{2}\right)+\left(6\right)\sqrt{2}+\left(\dfrac{385}{3}\right)\sqrt{2}-\dfrac{56}{5}-17+\dfrac{152}{9}\right)\\
&=&\left(\left(-18\right)\sqrt{2}\right)\left(-\dfrac{551}{180}+\left(\dfrac{941}{6}\right)\sqrt{2}\right)\\
&=&\left(\dfrac{551}{10}\right)\sqrt{2}+\left(-2823\right)\sqrt{4}\\
&=&\left(\dfrac{551}{10}\right)\sqrt{2}-5646\\
\end{eqnarray*}