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 \( X=\left(\left(-5\right)\sqrt{50}+\left(-\dfrac{19}{9}\right)\sqrt{50}+\left(0\right)\sqrt{4}\right)-\left(\left(\dfrac{23}{2}\right)\sqrt{50}+\dfrac{19}{2}\right)\) et \( Y=\left(\dfrac{55}{7}\right)\sqrt{8}\) . 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(-5\right)\sqrt{50}+\left(-\dfrac{19}{9}\right)\sqrt{50}+\left(0\right)\sqrt{4}\right)-\left(\left(\dfrac{23}{2}\right)\sqrt{50}+\dfrac{19}{2}\right)\right)+\left(\left(\dfrac{55}{7}\right)\sqrt{8}\right)\\
&=&\left(\left(\left(-25\right)\sqrt{2}+\left(-\dfrac{95}{9}\right)\sqrt{2}+0\right)-\left(\left(\dfrac{115}{2}\right)\sqrt{2}+\dfrac{19}{2}\right)\right)+\left(\left(\dfrac{110}{7}\right)\sqrt{2}\right)\\
&=&\left(\left(-25\right)\sqrt{2}+\left(-\dfrac{95}{9}\right)\sqrt{2}+0\right)-\left(\left(\dfrac{115}{2}\right)\sqrt{2}+\dfrac{19}{2}\right)+\left(\dfrac{110}{7}\right)\sqrt{2}\\
&=&\left(-\dfrac{9745}{126}\right)\sqrt{2}-\dfrac{19}{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(-5\right)\sqrt{50}+\left(-\dfrac{19}{9}\right)\sqrt{50}+\left(0\right)\sqrt{4}\right)-\left(\left(\dfrac{23}{2}\right)\sqrt{50}+\dfrac{19}{2}\right)\right)-\left(\left(\dfrac{55}{7}\right)\sqrt{8}\right)\\
&=&\left(\left(\left(-25\right)\sqrt{2}+\left(-\dfrac{95}{9}\right)\sqrt{2}+0\right)-\left(\left(\dfrac{115}{2}\right)\sqrt{2}+\dfrac{19}{2}\right)\right)-\left(\left(\dfrac{110}{7}\right)\sqrt{2}\right)\\
&=&\left(\left(-\dfrac{1675}{18}\right)\sqrt{2}-\dfrac{19}{2}\right)-\left(\left(\dfrac{110}{7}\right)\sqrt{2}\right)\\
&=&\left(-\dfrac{1675}{18}\right)\sqrt{2}-\dfrac{19}{2}+\left(-\dfrac{110}{7}\right)\sqrt{2}\\
&=&\left(-\dfrac{13705}{126}\right)\sqrt{2}-\dfrac{19}{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(-5\right)\sqrt{50}+\left(-\dfrac{19}{9}\right)\sqrt{50}+\left(0\right)\sqrt{4}\right)-\left(\left(\dfrac{23}{2}\right)\sqrt{50}+\dfrac{19}{2}\right)\right)\times\left(\left(\dfrac{55}{7}\right)\sqrt{8}\right)\\
&=&\left(\left(\left(-25\right)\sqrt{2}+\left(-\dfrac{95}{9}\right)\sqrt{2}+0\right)-\left(\left(\dfrac{115}{2}\right)\sqrt{2}+\dfrac{19}{2}\right)\right)\times\left(\left(\dfrac{110}{7}\right)\sqrt{2}\right)\\
&=&\left(\left(-\dfrac{1675}{18}\right)\sqrt{2}-\dfrac{19}{2}\right)\left(\left(\dfrac{110}{7}\right)\sqrt{2}\right)\\
&=&\left(-\dfrac{92125}{63}\right)\sqrt{4}+\left(-\dfrac{1045}{7}\right)\sqrt{2}\\
&=&-\dfrac{184250}{63}+\left(-\dfrac{1045}{7}\right)\sqrt{2}\\
\end{eqnarray*}