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 \( X=\left(\left(-6\right)\sqrt{8}\right)-\left(\left(-\dfrac{11}{3}\right)\sqrt{50}\right)-\left(\left(-\dfrac{4}{9}\right)\sqrt{18}\right)-\dfrac{62}{7}\) et \( Y=\left(\left(\dfrac{16}{3}\right)\sqrt{8}+\left(0\right)\sqrt{50}+\left(-8\right)\sqrt{18}\right)-\left(\left(-\dfrac{73}{7}\right)\sqrt{8}+\left(\dfrac{57}{2}\right)\sqrt{8}+\left(\dfrac{11}{2}\right)\sqrt{8}+\left(-4\right)\sqrt{18}\right)-\left(\left(-\dfrac{31}{2}\right)\sqrt{8}\right)\) . 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(-6\right)\sqrt{8}\right)-\left(\left(-\dfrac{11}{3}\right)\sqrt{50}\right)-\left(\left(-\dfrac{4}{9}\right)\sqrt{18}\right)-\dfrac{62}{7}\right)+\left(\left(\left(\dfrac{16}{3}\right)\sqrt{8}+\left(0\right)\sqrt{50}+\left(-8\right)\sqrt{18}\right)-\left(\left(-\dfrac{73}{7}\right)\sqrt{8}+\left(\dfrac{57}{2}\right)\sqrt{8}+\left(\dfrac{11}{2}\right)\sqrt{8}+\left(-4\right)\sqrt{18}\right)-\left(\left(-\dfrac{31}{2}\right)\sqrt{8}\right)\right)\\
&=&\left(\left(\left(-12\right)\sqrt{2}\right)-\left(\left(-\dfrac{55}{3}\right)\sqrt{2}\right)-\left(\left(-\dfrac{4}{3}\right)\sqrt{2}\right)-\dfrac{62}{7}\right)+\left(\left(\left(\dfrac{32}{3}\right)\sqrt{2}+\left(0\right)\sqrt{2}+\left(-24\right)\sqrt{2}\right)-\left(\left(-\dfrac{146}{7}\right)\sqrt{2}+\left(57\right)\sqrt{2}+\left(11\right)\sqrt{2}+\left(-12\right)\sqrt{2}\right)-\left(\left(-31\right)\sqrt{2}\right)\right)\\
&=&\left(\left(-12\right)\sqrt{2}\right)-\left(\left(-\dfrac{55}{3}\right)\sqrt{2}\right)-\left(\left(-\dfrac{4}{3}\right)\sqrt{2}\right)-\dfrac{62}{7}+\left(\left(\dfrac{32}{3}\right)\sqrt{2}+\left(0\right)\sqrt{2}+\left(-24\right)\sqrt{2}\right)-\left(\left(-\dfrac{146}{7}\right)\sqrt{2}+\left(57\right)\sqrt{2}+\left(11\right)\sqrt{2}+\left(-12\right)\sqrt{2}\right)-\left(\left(-31\right)\sqrt{2}\right)\\
&=&\left(-\dfrac{206}{21}\right)\sqrt{2}-\dfrac{62}{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(-6\right)\sqrt{8}\right)-\left(\left(-\dfrac{11}{3}\right)\sqrt{50}\right)-\left(\left(-\dfrac{4}{9}\right)\sqrt{18}\right)-\dfrac{62}{7}\right)-\left(\left(\left(\dfrac{16}{3}\right)\sqrt{8}+\left(0\right)\sqrt{50}+\left(-8\right)\sqrt{18}\right)-\left(\left(-\dfrac{73}{7}\right)\sqrt{8}+\left(\dfrac{57}{2}\right)\sqrt{8}+\left(\dfrac{11}{2}\right)\sqrt{8}+\left(-4\right)\sqrt{18}\right)-\left(\left(-\dfrac{31}{2}\right)\sqrt{8}\right)\right)\\
&=&\left(\left(\left(-12\right)\sqrt{2}\right)-\left(\left(-\dfrac{55}{3}\right)\sqrt{2}\right)-\left(\left(-\dfrac{4}{3}\right)\sqrt{2}\right)-\dfrac{62}{7}\right)-\left(\left(\left(\dfrac{32}{3}\right)\sqrt{2}+\left(0\right)\sqrt{2}+\left(-24\right)\sqrt{2}\right)-\left(\left(-\dfrac{146}{7}\right)\sqrt{2}+\left(57\right)\sqrt{2}+\left(11\right)\sqrt{2}+\left(-12\right)\sqrt{2}\right)-\left(\left(-31\right)\sqrt{2}\right)\right)\\
&=&\left(\left(\dfrac{23}{3}\right)\sqrt{2}-\dfrac{62}{7}\right)-\left(\left(-\dfrac{367}{21}\right)\sqrt{2}\right)\\
&=&\left(\dfrac{23}{3}\right)\sqrt{2}-\dfrac{62}{7}+\left(\dfrac{367}{21}\right)\sqrt{2}\\
&=&\left(\dfrac{176}{7}\right)\sqrt{2}-\dfrac{62}{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(-6\right)\sqrt{8}\right)-\left(\left(-\dfrac{11}{3}\right)\sqrt{50}\right)-\left(\left(-\dfrac{4}{9}\right)\sqrt{18}\right)-\dfrac{62}{7}\right)\times\left(\left(\left(\dfrac{16}{3}\right)\sqrt{8}+\left(0\right)\sqrt{50}+\left(-8\right)\sqrt{18}\right)-\left(\left(-\dfrac{73}{7}\right)\sqrt{8}+\left(\dfrac{57}{2}\right)\sqrt{8}+\left(\dfrac{11}{2}\right)\sqrt{8}+\left(-4\right)\sqrt{18}\right)-\left(\left(-\dfrac{31}{2}\right)\sqrt{8}\right)\right)\\
&=&\left(\left(\left(-12\right)\sqrt{2}\right)-\left(\left(-\dfrac{55}{3}\right)\sqrt{2}\right)-\left(\left(-\dfrac{4}{3}\right)\sqrt{2}\right)-\dfrac{62}{7}\right)\times\left(\left(\left(\dfrac{32}{3}\right)\sqrt{2}+\left(0\right)\sqrt{2}+\left(-24\right)\sqrt{2}\right)-\left(\left(-\dfrac{146}{7}\right)\sqrt{2}+\left(57\right)\sqrt{2}+\left(11\right)\sqrt{2}+\left(-12\right)\sqrt{2}\right)-\left(\left(-31\right)\sqrt{2}\right)\right)\\
&=&\left(\left(\dfrac{23}{3}\right)\sqrt{2}-\dfrac{62}{7}\right)\left(\left(-\dfrac{367}{21}\right)\sqrt{2}\right)\\
&=&\left(-\dfrac{8441}{63}\right)\sqrt{4}+\left(\dfrac{22754}{147}\right)\sqrt{2}\\
&=&-\dfrac{16882}{63}+\left(\dfrac{22754}{147}\right)\sqrt{2}\\
\end{eqnarray*}