L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(\left(\left(-\dfrac{49}{6}\right)\sqrt{75}\right)-\dfrac{17}{4}-\left(\left(\dfrac{31}{5}\right)\sqrt{12}\right)-\left(\left(-\dfrac{29}{4}\right)\sqrt{27}\right)\right)-\left(-\dfrac{47}{5}-\dfrac{36}{7}\right)\) et \( Y=6\) . 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(-\dfrac{49}{6}\right)\sqrt{75}\right)-\dfrac{17}{4}-\left(\left(\dfrac{31}{5}\right)\sqrt{12}\right)-\left(\left(-\dfrac{29}{4}\right)\sqrt{27}\right)\right)-\left(-\dfrac{47}{5}-\dfrac{36}{7}\right)\right)+\left(6\right)\\
&=&\left(\left(\left(\left(-\dfrac{245}{6}\right)\sqrt{3}\right)-\dfrac{17}{4}-\left(\left(\dfrac{62}{5}\right)\sqrt{3}\right)-\left(\left(-\dfrac{87}{4}\right)\sqrt{3}\right)\right)-\left(-\dfrac{47}{5}-\dfrac{36}{7}\right)\right)+\left(6\right)\\
&=&\left(\left(\left(-\dfrac{245}{6}\right)\sqrt{3}\right)-\dfrac{17}{4}-\left(\left(\dfrac{62}{5}\right)\sqrt{3}\right)-\left(\left(-\dfrac{87}{4}\right)\sqrt{3}\right)\right)-\left(-\dfrac{47}{5}-\dfrac{36}{7}\right)+6\\
&=&\left(-\dfrac{1889}{60}\right)\sqrt{3}+\dfrac{2281}{140}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(\left(-\dfrac{49}{6}\right)\sqrt{75}\right)-\dfrac{17}{4}-\left(\left(\dfrac{31}{5}\right)\sqrt{12}\right)-\left(\left(-\dfrac{29}{4}\right)\sqrt{27}\right)\right)-\left(-\dfrac{47}{5}-\dfrac{36}{7}\right)\right)-\left(6\right)\\
&=&\left(\left(\left(\left(-\dfrac{245}{6}\right)\sqrt{3}\right)-\dfrac{17}{4}-\left(\left(\dfrac{62}{5}\right)\sqrt{3}\right)-\left(\left(-\dfrac{87}{4}\right)\sqrt{3}\right)\right)-\left(-\dfrac{47}{5}-\dfrac{36}{7}\right)\right)-\left(6\right)\\
&=&\left(\left(-\dfrac{1889}{60}\right)\sqrt{3}+\dfrac{1441}{140}\right)-\left(6\right)\\
&=&\left(-\dfrac{1889}{60}\right)\sqrt{3}+\dfrac{1441}{140}+-6\\
&=&\left(-\dfrac{1889}{60}\right)\sqrt{3}+\dfrac{601}{140}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(\left(-\dfrac{49}{6}\right)\sqrt{75}\right)-\dfrac{17}{4}-\left(\left(\dfrac{31}{5}\right)\sqrt{12}\right)-\left(\left(-\dfrac{29}{4}\right)\sqrt{27}\right)\right)-\left(-\dfrac{47}{5}-\dfrac{36}{7}\right)\right)\times\left(6\right)\\
&=&\left(\left(\left(\left(-\dfrac{245}{6}\right)\sqrt{3}\right)-\dfrac{17}{4}-\left(\left(\dfrac{62}{5}\right)\sqrt{3}\right)-\left(\left(-\dfrac{87}{4}\right)\sqrt{3}\right)\right)-\left(-\dfrac{47}{5}-\dfrac{36}{7}\right)\right)\times\left(6\right)\\
&=&\left(\left(-\dfrac{1889}{60}\right)\sqrt{3}+\dfrac{1441}{140}\right)\left(6\right)\\
&=&\left(-\dfrac{1889}{10}\right)\sqrt{3}+\dfrac{4323}{70}\\
&=&\left(-\dfrac{1889}{10}\right)\sqrt{3}+\dfrac{4323}{70}\\
\end{eqnarray*}