L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(\left(\left(9\right)\sqrt{18}\right)-\dfrac{10}{3}\right)-\left(1-\dfrac{35}{4}-\left(\left(-\dfrac{39}{4}\right)\sqrt{18}\right)-\left(\left(\dfrac{59}{5}\right)\sqrt{50}\right)\right)-\left(\left(\dfrac{53}{8}\right)\sqrt{18}\right)-\left(\left(\dfrac{46}{7}\right)\sqrt{50}\right)\) et \( Y=\left(7\right)\sqrt{18}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(\left(\left(9\right)\sqrt{18}\right)-\dfrac{10}{3}\right)-\left(1-\dfrac{35}{4}-\left(\left(-\dfrac{39}{4}\right)\sqrt{18}\right)-\left(\left(\dfrac{59}{5}\right)\sqrt{50}\right)\right)-\left(\left(\dfrac{53}{8}\right)\sqrt{18}\right)-\left(\left(\dfrac{46}{7}\right)\sqrt{50}\right)\right)+\left(\left(7\right)\sqrt{18}\right)\\
&=&\left(\left(\left(\left(27\right)\sqrt{2}\right)-\dfrac{10}{3}\right)-\left(1-\dfrac{35}{4}-\left(\left(-\dfrac{117}{4}\right)\sqrt{2}\right)-\left(\left(59\right)\sqrt{2}\right)\right)-\left(\left(\dfrac{159}{8}\right)\sqrt{2}\right)-\left(\left(\dfrac{230}{7}\right)\sqrt{2}\right)\right)+\left(\left(21\right)\sqrt{2}\right)\\
&=&\left(\left(\left(27\right)\sqrt{2}\right)-\dfrac{10}{3}\right)-\left(1-\dfrac{35}{4}-\left(\left(-\dfrac{117}{4}\right)\sqrt{2}\right)-\left(\left(59\right)\sqrt{2}\right)\right)-\left(\left(\dfrac{159}{8}\right)\sqrt{2}\right)-\left(\left(\dfrac{230}{7}\right)\sqrt{2}\right)+\left(21\right)\sqrt{2}\\
&=&\left(\dfrac{1401}{56}\right)\sqrt{2}+\dfrac{53}{12}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(\left(9\right)\sqrt{18}\right)-\dfrac{10}{3}\right)-\left(1-\dfrac{35}{4}-\left(\left(-\dfrac{39}{4}\right)\sqrt{18}\right)-\left(\left(\dfrac{59}{5}\right)\sqrt{50}\right)\right)-\left(\left(\dfrac{53}{8}\right)\sqrt{18}\right)-\left(\left(\dfrac{46}{7}\right)\sqrt{50}\right)\right)-\left(\left(7\right)\sqrt{18}\right)\\
&=&\left(\left(\left(\left(27\right)\sqrt{2}\right)-\dfrac{10}{3}\right)-\left(1-\dfrac{35}{4}-\left(\left(-\dfrac{117}{4}\right)\sqrt{2}\right)-\left(\left(59\right)\sqrt{2}\right)\right)-\left(\left(\dfrac{159}{8}\right)\sqrt{2}\right)-\left(\left(\dfrac{230}{7}\right)\sqrt{2}\right)\right)-\left(\left(21\right)\sqrt{2}\right)\\
&=&\left(\left(\dfrac{225}{56}\right)\sqrt{2}+\dfrac{53}{12}\right)-\left(\left(21\right)\sqrt{2}\right)\\
&=&\left(\dfrac{225}{56}\right)\sqrt{2}+\dfrac{53}{12}+\left(-21\right)\sqrt{2}\\
&=&\left(-\dfrac{951}{56}\right)\sqrt{2}+\dfrac{53}{12}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(\left(9\right)\sqrt{18}\right)-\dfrac{10}{3}\right)-\left(1-\dfrac{35}{4}-\left(\left(-\dfrac{39}{4}\right)\sqrt{18}\right)-\left(\left(\dfrac{59}{5}\right)\sqrt{50}\right)\right)-\left(\left(\dfrac{53}{8}\right)\sqrt{18}\right)-\left(\left(\dfrac{46}{7}\right)\sqrt{50}\right)\right)\times\left(\left(7\right)\sqrt{18}\right)\\
&=&\left(\left(\left(\left(27\right)\sqrt{2}\right)-\dfrac{10}{3}\right)-\left(1-\dfrac{35}{4}-\left(\left(-\dfrac{117}{4}\right)\sqrt{2}\right)-\left(\left(59\right)\sqrt{2}\right)\right)-\left(\left(\dfrac{159}{8}\right)\sqrt{2}\right)-\left(\left(\dfrac{230}{7}\right)\sqrt{2}\right)\right)\times\left(\left(21\right)\sqrt{2}\right)\\
&=&\left(\left(\dfrac{225}{56}\right)\sqrt{2}+\dfrac{53}{12}\right)\left(\left(21\right)\sqrt{2}\right)\\
&=&\left(\dfrac{675}{8}\right)\sqrt{4}+\left(\dfrac{371}{4}\right)\sqrt{2}\\
&=&\dfrac{675}{4}+\left(\dfrac{371}{4}\right)\sqrt{2}\\
\end{eqnarray*}