L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
Si vous regénérez la page (F5) les valeurs seront changées.
La correction se trouve en bas de page.
Exercice
Soit \( X=-\dfrac{33}{2}+\dfrac{25}{6}+3-\left(\left(-4\right)\sqrt{20}\right)-\left(\left(\dfrac{35}{3}\right)\sqrt{125}\right)-\left(\left(-\dfrac{1}{3}\right)\sqrt{125}\right)\) et \( Y=\left(7\right)\sqrt{125}+\left(9\right)\sqrt{25}+\left(\dfrac{24}{5}\right)\sqrt{25}+\dfrac{66}{7}+\left(\left(3\right)\sqrt{125}\right)-\left(\left(-8\right)\sqrt{125}\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(-\dfrac{33}{2}+\dfrac{25}{6}+3-\left(\left(-4\right)\sqrt{20}\right)-\left(\left(\dfrac{35}{3}\right)\sqrt{125}\right)-\left(\left(-\dfrac{1}{3}\right)\sqrt{125}\right)\right)+\left(\left(7\right)\sqrt{125}+\left(9\right)\sqrt{25}+\left(\dfrac{24}{5}\right)\sqrt{25}+\dfrac{66}{7}+\left(\left(3\right)\sqrt{125}\right)-\left(\left(-8\right)\sqrt{125}\right)\right)\\
&=&\left(-\dfrac{33}{2}+\dfrac{25}{6}+3-\left(\left(-8\right)\sqrt{5}\right)-\left(\left(\dfrac{175}{3}\right)\sqrt{5}\right)-\left(\left(-\dfrac{5}{3}\right)\sqrt{5}\right)\right)+\left(\left(35\right)\sqrt{5}+45+24+\dfrac{66}{7}+\left(\left(15\right)\sqrt{5}\right)-\left(\left(-40\right)\sqrt{5}\right)\right)\\
&=&-\dfrac{33}{2}+\dfrac{25}{6}+3-\left(\left(-8\right)\sqrt{5}\right)-\left(\left(\dfrac{175}{3}\right)\sqrt{5}\right)-\left(\left(-\dfrac{5}{3}\right)\sqrt{5}\right)+\left(35\right)\sqrt{5}+45+24+\dfrac{66}{7}+\left(\left(15\right)\sqrt{5}\right)-\left(\left(-40\right)\sqrt{5}\right)\\
&=&\dfrac{1451}{21}+\left(\dfrac{124}{3}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(-\dfrac{33}{2}+\dfrac{25}{6}+3-\left(\left(-4\right)\sqrt{20}\right)-\left(\left(\dfrac{35}{3}\right)\sqrt{125}\right)-\left(\left(-\dfrac{1}{3}\right)\sqrt{125}\right)\right)-\left(\left(7\right)\sqrt{125}+\left(9\right)\sqrt{25}+\left(\dfrac{24}{5}\right)\sqrt{25}+\dfrac{66}{7}+\left(\left(3\right)\sqrt{125}\right)-\left(\left(-8\right)\sqrt{125}\right)\right)\\
&=&\left(-\dfrac{33}{2}+\dfrac{25}{6}+3-\left(\left(-8\right)\sqrt{5}\right)-\left(\left(\dfrac{175}{3}\right)\sqrt{5}\right)-\left(\left(-\dfrac{5}{3}\right)\sqrt{5}\right)\right)-\left(\left(35\right)\sqrt{5}+45+24+\dfrac{66}{7}+\left(\left(15\right)\sqrt{5}\right)-\left(\left(-40\right)\sqrt{5}\right)\right)\\
&=&\left(-\dfrac{28}{3}+\left(-\dfrac{146}{3}\right)\sqrt{5}\right)-\left(\left(90\right)\sqrt{5}+\dfrac{549}{7}\right)\\
&=&-\dfrac{28}{3}+\left(-\dfrac{146}{3}\right)\sqrt{5}+\left(-90\right)\sqrt{5}-\dfrac{549}{7}\\
&=&-\dfrac{1843}{21}+\left(-\dfrac{416}{3}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(-\dfrac{33}{2}+\dfrac{25}{6}+3-\left(\left(-4\right)\sqrt{20}\right)-\left(\left(\dfrac{35}{3}\right)\sqrt{125}\right)-\left(\left(-\dfrac{1}{3}\right)\sqrt{125}\right)\right)\times\left(\left(7\right)\sqrt{125}+\left(9\right)\sqrt{25}+\left(\dfrac{24}{5}\right)\sqrt{25}+\dfrac{66}{7}+\left(\left(3\right)\sqrt{125}\right)-\left(\left(-8\right)\sqrt{125}\right)\right)\\
&=&\left(-\dfrac{33}{2}+\dfrac{25}{6}+3-\left(\left(-8\right)\sqrt{5}\right)-\left(\left(\dfrac{175}{3}\right)\sqrt{5}\right)-\left(\left(-\dfrac{5}{3}\right)\sqrt{5}\right)\right)\times\left(\left(35\right)\sqrt{5}+45+24+\dfrac{66}{7}+\left(\left(15\right)\sqrt{5}\right)-\left(\left(-40\right)\sqrt{5}\right)\right)\\
&=&\left(-\dfrac{28}{3}+\left(-\dfrac{146}{3}\right)\sqrt{5}\right)\left(\left(90\right)\sqrt{5}+\dfrac{549}{7}\right)\\
&=&\left(-\dfrac{32598}{7}\right)\sqrt{5}-732+\left(-4380\right)\sqrt{25}\\
&=&\left(-\dfrac{32598}{7}\right)\sqrt{5}-22632\\
\end{eqnarray*}