L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(\left(0\right)\sqrt{9}\right)-\left(\left(-5\right)\sqrt{75}+\dfrac{53}{9}\right)-\dfrac{2}{7}-\left(\dfrac{72}{7}-\left(\left(-\dfrac{11}{8}\right)\sqrt{9}\right)-\dfrac{38}{5}+\dfrac{18}{7}\right)-\left(\left(-\dfrac{37}{9}\right)\sqrt{27}\right)\) et \( Y=\left(0\right)\sqrt{27}\) . 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(0\right)\sqrt{9}\right)-\left(\left(-5\right)\sqrt{75}+\dfrac{53}{9}\right)-\dfrac{2}{7}-\left(\dfrac{72}{7}-\left(\left(-\dfrac{11}{8}\right)\sqrt{9}\right)-\dfrac{38}{5}+\dfrac{18}{7}\right)-\left(\left(-\dfrac{37}{9}\right)\sqrt{27}\right)\right)+\left(\left(0\right)\sqrt{27}\right)\\
&=&\left(0-\left(\left(-25\right)\sqrt{3}+\dfrac{53}{9}\right)-\dfrac{2}{7}-\left(\dfrac{72}{7}+\dfrac{33}{8}-\dfrac{38}{5}+\dfrac{18}{7}\right)-\left(\left(-\dfrac{37}{3}\right)\sqrt{3}\right)\right)+\left(\left(0\right)\sqrt{3}\right)\\
&=&0-\left(\left(-25\right)\sqrt{3}+\dfrac{53}{9}\right)-\dfrac{2}{7}-\left(\dfrac{72}{7}+\dfrac{33}{8}-\dfrac{38}{5}+\dfrac{18}{7}\right)-\left(\left(-\dfrac{37}{3}\right)\sqrt{3}\right)+\left(0\right)\sqrt{3}\\
&=&-\dfrac{39203}{2520}+\left(\dfrac{112}{3}\right)\sqrt{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(0\right)\sqrt{9}\right)-\left(\left(-5\right)\sqrt{75}+\dfrac{53}{9}\right)-\dfrac{2}{7}-\left(\dfrac{72}{7}-\left(\left(-\dfrac{11}{8}\right)\sqrt{9}\right)-\dfrac{38}{5}+\dfrac{18}{7}\right)-\left(\left(-\dfrac{37}{9}\right)\sqrt{27}\right)\right)-\left(\left(0\right)\sqrt{27}\right)\\
&=&\left(0-\left(\left(-25\right)\sqrt{3}+\dfrac{53}{9}\right)-\dfrac{2}{7}-\left(\dfrac{72}{7}+\dfrac{33}{8}-\dfrac{38}{5}+\dfrac{18}{7}\right)-\left(\left(-\dfrac{37}{3}\right)\sqrt{3}\right)\right)-\left(\left(0\right)\sqrt{3}\right)\\
&=&\left(-\dfrac{39203}{2520}+\left(\dfrac{112}{3}\right)\sqrt{3}\right)-\left(\left(0\right)\sqrt{3}\right)\\
&=&-\dfrac{39203}{2520}+\left(\dfrac{112}{3}\right)\sqrt{3}+\left(0\right)\sqrt{3}\\
&=&-\dfrac{39203}{2520}+\left(\dfrac{112}{3}\right)\sqrt{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(0\right)\sqrt{9}\right)-\left(\left(-5\right)\sqrt{75}+\dfrac{53}{9}\right)-\dfrac{2}{7}-\left(\dfrac{72}{7}-\left(\left(-\dfrac{11}{8}\right)\sqrt{9}\right)-\dfrac{38}{5}+\dfrac{18}{7}\right)-\left(\left(-\dfrac{37}{9}\right)\sqrt{27}\right)\right)\times\left(\left(0\right)\sqrt{27}\right)\\
&=&\left(0-\left(\left(-25\right)\sqrt{3}+\dfrac{53}{9}\right)-\dfrac{2}{7}-\left(\dfrac{72}{7}+\dfrac{33}{8}-\dfrac{38}{5}+\dfrac{18}{7}\right)-\left(\left(-\dfrac{37}{3}\right)\sqrt{3}\right)\right)\times\left(\left(0\right)\sqrt{3}\right)\\
&=&\left(-\dfrac{39203}{2520}+\left(\dfrac{112}{3}\right)\sqrt{3}\right)\left(\left(0\right)\sqrt{3}\right)\\
&=&\left(0\right)\sqrt{3}+\left(0\right)\sqrt{9}\\
&=&\left(0\right)\sqrt{3}+0\\
\end{eqnarray*}