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 \( X=-\dfrac{39}{7}\) et \( Y=\left(\left(-\dfrac{79}{3}\right)\sqrt{20}\right)-\left(\left(-\dfrac{5}{4}\right)\sqrt{20}\right)+\dfrac{5}{3}-4+\left(\dfrac{39}{4}\right)\sqrt{125}+\left(\left(-\dfrac{1}{8}\right)\sqrt{25}\right)-\left(\left(\dfrac{17}{2}\right)\sqrt{45}\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(-\dfrac{39}{7}\right)+\left(\left(\left(-\dfrac{79}{3}\right)\sqrt{20}\right)-\left(\left(-\dfrac{5}{4}\right)\sqrt{20}\right)+\dfrac{5}{3}-4+\left(\dfrac{39}{4}\right)\sqrt{125}+\left(\left(-\dfrac{1}{8}\right)\sqrt{25}\right)-\left(\left(\dfrac{17}{2}\right)\sqrt{45}\right)\right)\\
&=&\left(-\dfrac{39}{7}\right)+\left(\left(\left(-\dfrac{158}{3}\right)\sqrt{5}\right)-\left(\left(-\dfrac{5}{2}\right)\sqrt{5}\right)+\dfrac{5}{3}-4+\left(\dfrac{195}{4}\right)\sqrt{5}-\dfrac{5}{8}-\left(\left(\dfrac{51}{2}\right)\sqrt{5}\right)\right)\\
&=&-\dfrac{39}{7}+\left(\left(-\dfrac{158}{3}\right)\sqrt{5}\right)-\left(\left(-\dfrac{5}{2}\right)\sqrt{5}\right)+\dfrac{5}{3}-4+\left(\dfrac{195}{4}\right)\sqrt{5}-\dfrac{5}{8}-\left(\left(\dfrac{51}{2}\right)\sqrt{5}\right)\\
&=&-\dfrac{1433}{168}+\left(-\dfrac{323}{12}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(-\dfrac{39}{7}\right)-\left(\left(\left(-\dfrac{79}{3}\right)\sqrt{20}\right)-\left(\left(-\dfrac{5}{4}\right)\sqrt{20}\right)+\dfrac{5}{3}-4+\left(\dfrac{39}{4}\right)\sqrt{125}+\left(\left(-\dfrac{1}{8}\right)\sqrt{25}\right)-\left(\left(\dfrac{17}{2}\right)\sqrt{45}\right)\right)\\
&=&\left(-\dfrac{39}{7}\right)-\left(\left(\left(-\dfrac{158}{3}\right)\sqrt{5}\right)-\left(\left(-\dfrac{5}{2}\right)\sqrt{5}\right)+\dfrac{5}{3}-4+\left(\dfrac{195}{4}\right)\sqrt{5}-\dfrac{5}{8}-\left(\left(\dfrac{51}{2}\right)\sqrt{5}\right)\right)\\
&=&\left(-\dfrac{39}{7}\right)-\left(\left(-\dfrac{323}{12}\right)\sqrt{5}-\dfrac{71}{24}\right)\\
&=&-\dfrac{39}{7}+\left(\dfrac{323}{12}\right)\sqrt{5}+\dfrac{71}{24}\\
&=&-\dfrac{439}{168}+\left(\dfrac{323}{12}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(-\dfrac{39}{7}\right)\times\left(\left(\left(-\dfrac{79}{3}\right)\sqrt{20}\right)-\left(\left(-\dfrac{5}{4}\right)\sqrt{20}\right)+\dfrac{5}{3}-4+\left(\dfrac{39}{4}\right)\sqrt{125}+\left(\left(-\dfrac{1}{8}\right)\sqrt{25}\right)-\left(\left(\dfrac{17}{2}\right)\sqrt{45}\right)\right)\\
&=&\left(-\dfrac{39}{7}\right)\times\left(\left(\left(-\dfrac{158}{3}\right)\sqrt{5}\right)-\left(\left(-\dfrac{5}{2}\right)\sqrt{5}\right)+\dfrac{5}{3}-4+\left(\dfrac{195}{4}\right)\sqrt{5}-\dfrac{5}{8}-\left(\left(\dfrac{51}{2}\right)\sqrt{5}\right)\right)\\
&=&\left(-\dfrac{39}{7}\right)\left(\left(-\dfrac{323}{12}\right)\sqrt{5}-\dfrac{71}{24}\right)\\
&=&\left(\dfrac{4199}{28}\right)\sqrt{5}+\dfrac{923}{56}\\
&=&\left(\dfrac{4199}{28}\right)\sqrt{5}+\dfrac{923}{56}\\
\end{eqnarray*}