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 \( X=\left(\dfrac{22}{9}\right)\sqrt{4}\) et \( Y=\left(\left(\dfrac{73}{2}\right)\sqrt{50}\right)-\left(\left(8\right)\sqrt{8}\right)-\left(\left(\dfrac{13}{9}\right)\sqrt{4}\right)-\dfrac{19}{6}-\dfrac{69}{5}+\left(-\dfrac{65}{2}\right)\sqrt{8}+\left(-2\right)\sqrt{18}-\dfrac{13}{3}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(\dfrac{22}{9}\right)\sqrt{4}\right)+\left(\left(\left(\dfrac{73}{2}\right)\sqrt{50}\right)-\left(\left(8\right)\sqrt{8}\right)-\left(\left(\dfrac{13}{9}\right)\sqrt{4}\right)-\dfrac{19}{6}-\dfrac{69}{5}+\left(-\dfrac{65}{2}\right)\sqrt{8}+\left(-2\right)\sqrt{18}-\dfrac{13}{3}\right)\\
&=&\left(\dfrac{44}{9}\right)+\left(\left(\left(\dfrac{365}{2}\right)\sqrt{2}\right)-\left(\left(16\right)\sqrt{2}\right)-\dfrac{26}{9}-\dfrac{19}{6}-\dfrac{69}{5}+\left(-65\right)\sqrt{2}+\left(-6\right)\sqrt{2}-\dfrac{13}{3}\right)\\
&=&\dfrac{44}{9}+\left(\left(\dfrac{365}{2}\right)\sqrt{2}\right)-\left(\left(16\right)\sqrt{2}\right)-\dfrac{26}{9}-\dfrac{19}{6}-\dfrac{69}{5}+\left(-65\right)\sqrt{2}+\left(-6\right)\sqrt{2}-\dfrac{13}{3}\\
&=&-\dfrac{193}{10}+\left(\dfrac{191}{2}\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\dfrac{22}{9}\right)\sqrt{4}\right)-\left(\left(\left(\dfrac{73}{2}\right)\sqrt{50}\right)-\left(\left(8\right)\sqrt{8}\right)-\left(\left(\dfrac{13}{9}\right)\sqrt{4}\right)-\dfrac{19}{6}-\dfrac{69}{5}+\left(-\dfrac{65}{2}\right)\sqrt{8}+\left(-2\right)\sqrt{18}-\dfrac{13}{3}\right)\\
&=&\left(\dfrac{44}{9}\right)-\left(\left(\left(\dfrac{365}{2}\right)\sqrt{2}\right)-\left(\left(16\right)\sqrt{2}\right)-\dfrac{26}{9}-\dfrac{19}{6}-\dfrac{69}{5}+\left(-65\right)\sqrt{2}+\left(-6\right)\sqrt{2}-\dfrac{13}{3}\right)\\
&=&\left(\dfrac{44}{9}\right)-\left(\left(\dfrac{191}{2}\right)\sqrt{2}-\dfrac{2177}{90}\right)\\
&=&\dfrac{44}{9}+\left(-\dfrac{191}{2}\right)\sqrt{2}+\dfrac{2177}{90}\\
&=&\dfrac{2617}{90}+\left(-\dfrac{191}{2}\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\dfrac{22}{9}\right)\sqrt{4}\right)\times\left(\left(\left(\dfrac{73}{2}\right)\sqrt{50}\right)-\left(\left(8\right)\sqrt{8}\right)-\left(\left(\dfrac{13}{9}\right)\sqrt{4}\right)-\dfrac{19}{6}-\dfrac{69}{5}+\left(-\dfrac{65}{2}\right)\sqrt{8}+\left(-2\right)\sqrt{18}-\dfrac{13}{3}\right)\\
&=&\left(\dfrac{44}{9}\right)\times\left(\left(\left(\dfrac{365}{2}\right)\sqrt{2}\right)-\left(\left(16\right)\sqrt{2}\right)-\dfrac{26}{9}-\dfrac{19}{6}-\dfrac{69}{5}+\left(-65\right)\sqrt{2}+\left(-6\right)\sqrt{2}-\dfrac{13}{3}\right)\\
&=&\left(\dfrac{44}{9}\right)\left(\left(\dfrac{191}{2}\right)\sqrt{2}-\dfrac{2177}{90}\right)\\
&=&\left(\dfrac{4202}{9}\right)\sqrt{2}-\dfrac{47894}{405}\\
&=&\left(\dfrac{4202}{9}\right)\sqrt{2}-\dfrac{47894}{405}\\
\end{eqnarray*}