L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(\left(\left(-\dfrac{19}{2}\right)\sqrt{175}\right)-\left(\left(-\dfrac{38}{9}\right)\sqrt{63}\right)\right)-\left(\left(-7\right)\sqrt{28}+\left(-3\right)\sqrt{28}\right)-\left(-6-\left(\left(\dfrac{15}{2}\right)\sqrt{28}\right)-\left(\left(-\dfrac{31}{7}\right)\sqrt{49}\right)\right)-\left(\left(\left(-9\right)\sqrt{63}\right)+\dfrac{47}{8}\right)\) et \( Y=\left(-\dfrac{66}{7}\right)\sqrt{28}\) . 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{19}{2}\right)\sqrt{175}\right)-\left(\left(-\dfrac{38}{9}\right)\sqrt{63}\right)\right)-\left(\left(-7\right)\sqrt{28}+\left(-3\right)\sqrt{28}\right)-\left(-6-\left(\left(\dfrac{15}{2}\right)\sqrt{28}\right)-\left(\left(-\dfrac{31}{7}\right)\sqrt{49}\right)\right)-\left(\left(\left(-9\right)\sqrt{63}\right)+\dfrac{47}{8}\right)\right)+\left(\left(-\dfrac{66}{7}\right)\sqrt{28}\right)\\
&=&\left(\left(\left(\left(-\dfrac{95}{2}\right)\sqrt{7}\right)-\left(\left(-\dfrac{38}{3}\right)\sqrt{7}\right)\right)-\left(\left(-14\right)\sqrt{7}+\left(-6\right)\sqrt{7}\right)-\left(-6-\left(\left(15\right)\sqrt{7}\right)+31\right)-\left(\left(\left(-27\right)\sqrt{7}\right)+\dfrac{47}{8}\right)\right)+\left(\left(-\dfrac{132}{7}\right)\sqrt{7}\right)\\
&=&\left(\left(\left(-\dfrac{95}{2}\right)\sqrt{7}\right)-\left(\left(-\dfrac{38}{3}\right)\sqrt{7}\right)\right)-\left(\left(-14\right)\sqrt{7}+\left(-6\right)\sqrt{7}\right)-\left(-6-\left(\left(15\right)\sqrt{7}\right)+31\right)-\left(\left(\left(-27\right)\sqrt{7}\right)+\dfrac{47}{8}\right)+\left(-\dfrac{132}{7}\right)\sqrt{7}\\
&=&\left(\dfrac{349}{42}\right)\sqrt{7}-\dfrac{247}{8}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(\left(-\dfrac{19}{2}\right)\sqrt{175}\right)-\left(\left(-\dfrac{38}{9}\right)\sqrt{63}\right)\right)-\left(\left(-7\right)\sqrt{28}+\left(-3\right)\sqrt{28}\right)-\left(-6-\left(\left(\dfrac{15}{2}\right)\sqrt{28}\right)-\left(\left(-\dfrac{31}{7}\right)\sqrt{49}\right)\right)-\left(\left(\left(-9\right)\sqrt{63}\right)+\dfrac{47}{8}\right)\right)-\left(\left(-\dfrac{66}{7}\right)\sqrt{28}\right)\\
&=&\left(\left(\left(\left(-\dfrac{95}{2}\right)\sqrt{7}\right)-\left(\left(-\dfrac{38}{3}\right)\sqrt{7}\right)\right)-\left(\left(-14\right)\sqrt{7}+\left(-6\right)\sqrt{7}\right)-\left(-6-\left(\left(15\right)\sqrt{7}\right)+31\right)-\left(\left(\left(-27\right)\sqrt{7}\right)+\dfrac{47}{8}\right)\right)-\left(\left(-\dfrac{132}{7}\right)\sqrt{7}\right)\\
&=&\left(\left(\dfrac{163}{6}\right)\sqrt{7}-\dfrac{247}{8}\right)-\left(\left(-\dfrac{132}{7}\right)\sqrt{7}\right)\\
&=&\left(\dfrac{163}{6}\right)\sqrt{7}-\dfrac{247}{8}+\left(\dfrac{132}{7}\right)\sqrt{7}\\
&=&\left(\dfrac{1933}{42}\right)\sqrt{7}-\dfrac{247}{8}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(\left(-\dfrac{19}{2}\right)\sqrt{175}\right)-\left(\left(-\dfrac{38}{9}\right)\sqrt{63}\right)\right)-\left(\left(-7\right)\sqrt{28}+\left(-3\right)\sqrt{28}\right)-\left(-6-\left(\left(\dfrac{15}{2}\right)\sqrt{28}\right)-\left(\left(-\dfrac{31}{7}\right)\sqrt{49}\right)\right)-\left(\left(\left(-9\right)\sqrt{63}\right)+\dfrac{47}{8}\right)\right)\times\left(\left(-\dfrac{66}{7}\right)\sqrt{28}\right)\\
&=&\left(\left(\left(\left(-\dfrac{95}{2}\right)\sqrt{7}\right)-\left(\left(-\dfrac{38}{3}\right)\sqrt{7}\right)\right)-\left(\left(-14\right)\sqrt{7}+\left(-6\right)\sqrt{7}\right)-\left(-6-\left(\left(15\right)\sqrt{7}\right)+31\right)-\left(\left(\left(-27\right)\sqrt{7}\right)+\dfrac{47}{8}\right)\right)\times\left(\left(-\dfrac{132}{7}\right)\sqrt{7}\right)\\
&=&\left(\left(\dfrac{163}{6}\right)\sqrt{7}-\dfrac{247}{8}\right)\left(\left(-\dfrac{132}{7}\right)\sqrt{7}\right)\\
&=&\left(-\dfrac{3586}{7}\right)\sqrt{49}+\left(\dfrac{8151}{14}\right)\sqrt{7}\\
&=&-3586+\left(\dfrac{8151}{14}\right)\sqrt{7}\\
\end{eqnarray*}