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 \( X=\left(\dfrac{39}{4}\right)\sqrt{4}\) et \( Y=\left(\left(-\dfrac{23}{7}\right)\sqrt{18}\right)-\left(\dfrac{72}{7}-\left(\left(\dfrac{33}{5}\right)\sqrt{4}\right)-\left(\left(\dfrac{81}{7}\right)\sqrt{50}\right)\right)-3\) . 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{39}{4}\right)\sqrt{4}\right)+\left(\left(\left(-\dfrac{23}{7}\right)\sqrt{18}\right)-\left(\dfrac{72}{7}-\left(\left(\dfrac{33}{5}\right)\sqrt{4}\right)-\left(\left(\dfrac{81}{7}\right)\sqrt{50}\right)\right)-3\right)\\
&=&\left(\dfrac{39}{2}\right)+\left(\left(\left(-\dfrac{69}{7}\right)\sqrt{2}\right)-\left(\dfrac{72}{7}-\dfrac{66}{5}-\left(\left(\dfrac{405}{7}\right)\sqrt{2}\right)\right)-3\right)\\
&=&\dfrac{39}{2}+\left(\left(-\dfrac{69}{7}\right)\sqrt{2}\right)-\left(\dfrac{72}{7}-\dfrac{66}{5}-\left(\left(\dfrac{405}{7}\right)\sqrt{2}\right)\right)-3\\
&=&\dfrac{1359}{70}+\left(48\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\dfrac{39}{4}\right)\sqrt{4}\right)-\left(\left(\left(-\dfrac{23}{7}\right)\sqrt{18}\right)-\left(\dfrac{72}{7}-\left(\left(\dfrac{33}{5}\right)\sqrt{4}\right)-\left(\left(\dfrac{81}{7}\right)\sqrt{50}\right)\right)-3\right)\\
&=&\left(\dfrac{39}{2}\right)-\left(\left(\left(-\dfrac{69}{7}\right)\sqrt{2}\right)-\left(\dfrac{72}{7}-\dfrac{66}{5}-\left(\left(\dfrac{405}{7}\right)\sqrt{2}\right)\right)-3\right)\\
&=&\left(\dfrac{39}{2}\right)-\left(\left(48\right)\sqrt{2}-\dfrac{3}{35}\right)\\
&=&\dfrac{39}{2}+\left(-48\right)\sqrt{2}+\dfrac{3}{35}\\
&=&\dfrac{1371}{70}+\left(-48\right)\sqrt{2}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\dfrac{39}{4}\right)\sqrt{4}\right)\times\left(\left(\left(-\dfrac{23}{7}\right)\sqrt{18}\right)-\left(\dfrac{72}{7}-\left(\left(\dfrac{33}{5}\right)\sqrt{4}\right)-\left(\left(\dfrac{81}{7}\right)\sqrt{50}\right)\right)-3\right)\\
&=&\left(\dfrac{39}{2}\right)\times\left(\left(\left(-\dfrac{69}{7}\right)\sqrt{2}\right)-\left(\dfrac{72}{7}-\dfrac{66}{5}-\left(\left(\dfrac{405}{7}\right)\sqrt{2}\right)\right)-3\right)\\
&=&\left(\dfrac{39}{2}\right)\left(\left(48\right)\sqrt{2}-\dfrac{3}{35}\right)\\
&=&\left(936\right)\sqrt{2}-\dfrac{117}{70}\\
&=&\left(936\right)\sqrt{2}-\dfrac{117}{70}\\
\end{eqnarray*}