L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(8\right)\sqrt{50}+\left(-4\right)\sqrt{8}+\left(-\dfrac{13}{7}\right)\sqrt{4}+\left(-\dfrac{35}{6}\right)\sqrt{50}+\left(\dfrac{79}{6}\right)\sqrt{8}+\left(\left(-\dfrac{23}{3}\right)\sqrt{4}\right)+\dfrac{71}{7}\) et \( Y=\left(\dfrac{7}{4}\right)\sqrt{4}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(8\right)\sqrt{50}+\left(-4\right)\sqrt{8}+\left(-\dfrac{13}{7}\right)\sqrt{4}+\left(-\dfrac{35}{6}\right)\sqrt{50}+\left(\dfrac{79}{6}\right)\sqrt{8}+\left(\left(-\dfrac{23}{3}\right)\sqrt{4}\right)+\dfrac{71}{7}\right)+\left(\left(\dfrac{7}{4}\right)\sqrt{4}\right)\\
&=&\left(\left(40\right)\sqrt{2}+\left(-8\right)\sqrt{2}-\dfrac{26}{7}+\left(-\dfrac{175}{6}\right)\sqrt{2}+\left(\dfrac{79}{3}\right)\sqrt{2}-\dfrac{46}{3}+\dfrac{71}{7}\right)+\left(\dfrac{7}{2}\right)\\
&=&\left(40\right)\sqrt{2}+\left(-8\right)\sqrt{2}-\dfrac{26}{7}+\left(-\dfrac{175}{6}\right)\sqrt{2}+\left(\dfrac{79}{3}\right)\sqrt{2}-\dfrac{46}{3}+\dfrac{71}{7}+\dfrac{7}{2}\\
&=&\left(\dfrac{175}{6}\right)\sqrt{2}-\dfrac{227}{42}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(8\right)\sqrt{50}+\left(-4\right)\sqrt{8}+\left(-\dfrac{13}{7}\right)\sqrt{4}+\left(-\dfrac{35}{6}\right)\sqrt{50}+\left(\dfrac{79}{6}\right)\sqrt{8}+\left(\left(-\dfrac{23}{3}\right)\sqrt{4}\right)+\dfrac{71}{7}\right)-\left(\left(\dfrac{7}{4}\right)\sqrt{4}\right)\\
&=&\left(\left(40\right)\sqrt{2}+\left(-8\right)\sqrt{2}-\dfrac{26}{7}+\left(-\dfrac{175}{6}\right)\sqrt{2}+\left(\dfrac{79}{3}\right)\sqrt{2}-\dfrac{46}{3}+\dfrac{71}{7}\right)-\left(\dfrac{7}{2}\right)\\
&=&\left(\left(\dfrac{175}{6}\right)\sqrt{2}-\dfrac{187}{21}\right)-\left(\dfrac{7}{2}\right)\\
&=&\left(\dfrac{175}{6}\right)\sqrt{2}-\dfrac{187}{21}+-\dfrac{7}{2}\\
&=&\left(\dfrac{175}{6}\right)\sqrt{2}-\dfrac{521}{42}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(8\right)\sqrt{50}+\left(-4\right)\sqrt{8}+\left(-\dfrac{13}{7}\right)\sqrt{4}+\left(-\dfrac{35}{6}\right)\sqrt{50}+\left(\dfrac{79}{6}\right)\sqrt{8}+\left(\left(-\dfrac{23}{3}\right)\sqrt{4}\right)+\dfrac{71}{7}\right)\times\left(\left(\dfrac{7}{4}\right)\sqrt{4}\right)\\
&=&\left(\left(40\right)\sqrt{2}+\left(-8\right)\sqrt{2}-\dfrac{26}{7}+\left(-\dfrac{175}{6}\right)\sqrt{2}+\left(\dfrac{79}{3}\right)\sqrt{2}-\dfrac{46}{3}+\dfrac{71}{7}\right)\times\left(\dfrac{7}{2}\right)\\
&=&\left(\left(\dfrac{175}{6}\right)\sqrt{2}-\dfrac{187}{21}\right)\left(\dfrac{7}{2}\right)\\
&=&\left(\dfrac{1225}{12}\right)\sqrt{2}-\dfrac{187}{6}\\
&=&\left(\dfrac{1225}{12}\right)\sqrt{2}-\dfrac{187}{6}\\
\end{eqnarray*}