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 \( X=\left(\left(-\dfrac{67}{2}\right)\sqrt{45}+\left(-\dfrac{69}{2}\right)\sqrt{25}+\left(-\dfrac{55}{3}\right)\sqrt{125}\right)-\left(\left(\left(0\right)\sqrt{45}\right)-\left(\left(\dfrac{69}{2}\right)\sqrt{125}\right)+6-\left(\left(-\dfrac{75}{4}\right)\sqrt{25}\right)\right)\) et \( Y=\left(-\dfrac{53}{7}\right)\sqrt{45}\) . 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(-\dfrac{67}{2}\right)\sqrt{45}+\left(-\dfrac{69}{2}\right)\sqrt{25}+\left(-\dfrac{55}{3}\right)\sqrt{125}\right)-\left(\left(\left(0\right)\sqrt{45}\right)-\left(\left(\dfrac{69}{2}\right)\sqrt{125}\right)+6-\left(\left(-\dfrac{75}{4}\right)\sqrt{25}\right)\right)\right)+\left(\left(-\dfrac{53}{7}\right)\sqrt{45}\right)\\
&=&\left(\left(\left(-\dfrac{201}{2}\right)\sqrt{5}-\dfrac{345}{2}+\left(-\dfrac{275}{3}\right)\sqrt{5}\right)-\left(\left(\left(0\right)\sqrt{5}\right)-\left(\left(\dfrac{345}{2}\right)\sqrt{5}\right)+6+\dfrac{375}{4}\right)\right)+\left(\left(-\dfrac{159}{7}\right)\sqrt{5}\right)\\
&=&\left(\left(-\dfrac{201}{2}\right)\sqrt{5}-\dfrac{345}{2}+\left(-\dfrac{275}{3}\right)\sqrt{5}\right)-\left(\left(\left(0\right)\sqrt{5}\right)-\left(\left(\dfrac{345}{2}\right)\sqrt{5}\right)+6+\dfrac{375}{4}\right)+\left(-\dfrac{159}{7}\right)\sqrt{5}\\
&=&\left(-\dfrac{890}{21}\right)\sqrt{5}-\dfrac{1089}{4}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(-\dfrac{67}{2}\right)\sqrt{45}+\left(-\dfrac{69}{2}\right)\sqrt{25}+\left(-\dfrac{55}{3}\right)\sqrt{125}\right)-\left(\left(\left(0\right)\sqrt{45}\right)-\left(\left(\dfrac{69}{2}\right)\sqrt{125}\right)+6-\left(\left(-\dfrac{75}{4}\right)\sqrt{25}\right)\right)\right)-\left(\left(-\dfrac{53}{7}\right)\sqrt{45}\right)\\
&=&\left(\left(\left(-\dfrac{201}{2}\right)\sqrt{5}-\dfrac{345}{2}+\left(-\dfrac{275}{3}\right)\sqrt{5}\right)-\left(\left(\left(0\right)\sqrt{5}\right)-\left(\left(\dfrac{345}{2}\right)\sqrt{5}\right)+6+\dfrac{375}{4}\right)\right)-\left(\left(-\dfrac{159}{7}\right)\sqrt{5}\right)\\
&=&\left(\left(-\dfrac{59}{3}\right)\sqrt{5}-\dfrac{1089}{4}\right)-\left(\left(-\dfrac{159}{7}\right)\sqrt{5}\right)\\
&=&\left(-\dfrac{59}{3}\right)\sqrt{5}-\dfrac{1089}{4}+\left(\dfrac{159}{7}\right)\sqrt{5}\\
&=&\left(\dfrac{64}{21}\right)\sqrt{5}-\dfrac{1089}{4}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(-\dfrac{67}{2}\right)\sqrt{45}+\left(-\dfrac{69}{2}\right)\sqrt{25}+\left(-\dfrac{55}{3}\right)\sqrt{125}\right)-\left(\left(\left(0\right)\sqrt{45}\right)-\left(\left(\dfrac{69}{2}\right)\sqrt{125}\right)+6-\left(\left(-\dfrac{75}{4}\right)\sqrt{25}\right)\right)\right)\times\left(\left(-\dfrac{53}{7}\right)\sqrt{45}\right)\\
&=&\left(\left(\left(-\dfrac{201}{2}\right)\sqrt{5}-\dfrac{345}{2}+\left(-\dfrac{275}{3}\right)\sqrt{5}\right)-\left(\left(\left(0\right)\sqrt{5}\right)-\left(\left(\dfrac{345}{2}\right)\sqrt{5}\right)+6+\dfrac{375}{4}\right)\right)\times\left(\left(-\dfrac{159}{7}\right)\sqrt{5}\right)\\
&=&\left(\left(-\dfrac{59}{3}\right)\sqrt{5}-\dfrac{1089}{4}\right)\left(\left(-\dfrac{159}{7}\right)\sqrt{5}\right)\\
&=&\left(\dfrac{3127}{7}\right)\sqrt{25}+\left(\dfrac{173151}{28}\right)\sqrt{5}\\
&=&\dfrac{15635}{7}+\left(\dfrac{173151}{28}\right)\sqrt{5}\\
\end{eqnarray*}