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 \( X=\left(\left(\left(\dfrac{9}{2}\right)\sqrt{20}\right)-\left(\left(\dfrac{71}{3}\right)\sqrt{125}\right)-\left(\left(\dfrac{31}{9}\right)\sqrt{125}\right)-\left(\left(-\dfrac{49}{2}\right)\sqrt{125}\right)\right)-\left(\left(-\dfrac{22}{7}\right)\sqrt{125}\right)-\left(\left(-\dfrac{25}{3}\right)\sqrt{25}+\left(0\right)\sqrt{20}\right)\) et \( Y=\left(-\dfrac{37}{6}\right)\sqrt{25}\) . 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{9}{2}\right)\sqrt{20}\right)-\left(\left(\dfrac{71}{3}\right)\sqrt{125}\right)-\left(\left(\dfrac{31}{9}\right)\sqrt{125}\right)-\left(\left(-\dfrac{49}{2}\right)\sqrt{125}\right)\right)-\left(\left(-\dfrac{22}{7}\right)\sqrt{125}\right)-\left(\left(-\dfrac{25}{3}\right)\sqrt{25}+\left(0\right)\sqrt{20}\right)\right)+\left(\left(-\dfrac{37}{6}\right)\sqrt{25}\right)\\
&=&\left(\left(\left(\left(9\right)\sqrt{5}\right)-\left(\left(\dfrac{355}{3}\right)\sqrt{5}\right)-\left(\left(\dfrac{155}{9}\right)\sqrt{5}\right)-\left(\left(-\dfrac{245}{2}\right)\sqrt{5}\right)\right)-\left(\left(-\dfrac{110}{7}\right)\sqrt{5}\right)-\left(-\dfrac{125}{3}+\left(0\right)\sqrt{5}\right)\right)+\left(-\dfrac{185}{6}\right)\\
&=&\left(\left(\left(9\right)\sqrt{5}\right)-\left(\left(\dfrac{355}{3}\right)\sqrt{5}\right)-\left(\left(\dfrac{155}{9}\right)\sqrt{5}\right)-\left(\left(-\dfrac{245}{2}\right)\sqrt{5}\right)\right)-\left(\left(-\dfrac{110}{7}\right)\sqrt{5}\right)-\left(-\dfrac{125}{3}+\left(0\right)\sqrt{5}\right)-\dfrac{185}{6}\\
&=&\left(\dfrac{1469}{126}\right)\sqrt{5}+\dfrac{65}{6}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(\left(\dfrac{9}{2}\right)\sqrt{20}\right)-\left(\left(\dfrac{71}{3}\right)\sqrt{125}\right)-\left(\left(\dfrac{31}{9}\right)\sqrt{125}\right)-\left(\left(-\dfrac{49}{2}\right)\sqrt{125}\right)\right)-\left(\left(-\dfrac{22}{7}\right)\sqrt{125}\right)-\left(\left(-\dfrac{25}{3}\right)\sqrt{25}+\left(0\right)\sqrt{20}\right)\right)-\left(\left(-\dfrac{37}{6}\right)\sqrt{25}\right)\\
&=&\left(\left(\left(\left(9\right)\sqrt{5}\right)-\left(\left(\dfrac{355}{3}\right)\sqrt{5}\right)-\left(\left(\dfrac{155}{9}\right)\sqrt{5}\right)-\left(\left(-\dfrac{245}{2}\right)\sqrt{5}\right)\right)-\left(\left(-\dfrac{110}{7}\right)\sqrt{5}\right)-\left(-\dfrac{125}{3}+\left(0\right)\sqrt{5}\right)\right)-\left(-\dfrac{185}{6}\right)\\
&=&\left(\left(\dfrac{1469}{126}\right)\sqrt{5}+\dfrac{125}{3}\right)-\left(-\dfrac{185}{6}\right)\\
&=&\left(\dfrac{1469}{126}\right)\sqrt{5}+\dfrac{125}{3}+\dfrac{185}{6}\\
&=&\left(\dfrac{1469}{126}\right)\sqrt{5}+\dfrac{145}{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(\left(\dfrac{9}{2}\right)\sqrt{20}\right)-\left(\left(\dfrac{71}{3}\right)\sqrt{125}\right)-\left(\left(\dfrac{31}{9}\right)\sqrt{125}\right)-\left(\left(-\dfrac{49}{2}\right)\sqrt{125}\right)\right)-\left(\left(-\dfrac{22}{7}\right)\sqrt{125}\right)-\left(\left(-\dfrac{25}{3}\right)\sqrt{25}+\left(0\right)\sqrt{20}\right)\right)\times\left(\left(-\dfrac{37}{6}\right)\sqrt{25}\right)\\
&=&\left(\left(\left(\left(9\right)\sqrt{5}\right)-\left(\left(\dfrac{355}{3}\right)\sqrt{5}\right)-\left(\left(\dfrac{155}{9}\right)\sqrt{5}\right)-\left(\left(-\dfrac{245}{2}\right)\sqrt{5}\right)\right)-\left(\left(-\dfrac{110}{7}\right)\sqrt{5}\right)-\left(-\dfrac{125}{3}+\left(0\right)\sqrt{5}\right)\right)\times\left(-\dfrac{185}{6}\right)\\
&=&\left(\left(\dfrac{1469}{126}\right)\sqrt{5}+\dfrac{125}{3}\right)\left(-\dfrac{185}{6}\right)\\
&=&\left(-\dfrac{271765}{756}\right)\sqrt{5}-\dfrac{23125}{18}\\
&=&\left(-\dfrac{271765}{756}\right)\sqrt{5}-\dfrac{23125}{18}\\
\end{eqnarray*}