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 \( X=\left(\dfrac{49}{5}\right)\sqrt{28}+\left(-\dfrac{71}{4}\right)\sqrt{49}+\left(\dfrac{49}{5}\right)\sqrt{28}\) et \( Y=\left(-\dfrac{23}{2}\right)\sqrt{63}\) . 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{49}{5}\right)\sqrt{28}+\left(-\dfrac{71}{4}\right)\sqrt{49}+\left(\dfrac{49}{5}\right)\sqrt{28}\right)+\left(\left(-\dfrac{23}{2}\right)\sqrt{63}\right)\\
&=&\left(\left(\dfrac{98}{5}\right)\sqrt{7}-\dfrac{497}{4}+\left(\dfrac{98}{5}\right)\sqrt{7}\right)+\left(\left(-\dfrac{69}{2}\right)\sqrt{7}\right)\\
&=&\left(\dfrac{98}{5}\right)\sqrt{7}-\dfrac{497}{4}+\left(\dfrac{98}{5}\right)\sqrt{7}+\left(-\dfrac{69}{2}\right)\sqrt{7}\\
&=&\left(\dfrac{47}{10}\right)\sqrt{7}-\dfrac{497}{4}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\dfrac{49}{5}\right)\sqrt{28}+\left(-\dfrac{71}{4}\right)\sqrt{49}+\left(\dfrac{49}{5}\right)\sqrt{28}\right)-\left(\left(-\dfrac{23}{2}\right)\sqrt{63}\right)\\
&=&\left(\left(\dfrac{98}{5}\right)\sqrt{7}-\dfrac{497}{4}+\left(\dfrac{98}{5}\right)\sqrt{7}\right)-\left(\left(-\dfrac{69}{2}\right)\sqrt{7}\right)\\
&=&\left(\left(\dfrac{196}{5}\right)\sqrt{7}-\dfrac{497}{4}\right)-\left(\left(-\dfrac{69}{2}\right)\sqrt{7}\right)\\
&=&\left(\dfrac{196}{5}\right)\sqrt{7}-\dfrac{497}{4}+\left(\dfrac{69}{2}\right)\sqrt{7}\\
&=&\left(\dfrac{737}{10}\right)\sqrt{7}-\dfrac{497}{4}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\dfrac{49}{5}\right)\sqrt{28}+\left(-\dfrac{71}{4}\right)\sqrt{49}+\left(\dfrac{49}{5}\right)\sqrt{28}\right)\times\left(\left(-\dfrac{23}{2}\right)\sqrt{63}\right)\\
&=&\left(\left(\dfrac{98}{5}\right)\sqrt{7}-\dfrac{497}{4}+\left(\dfrac{98}{5}\right)\sqrt{7}\right)\times\left(\left(-\dfrac{69}{2}\right)\sqrt{7}\right)\\
&=&\left(\left(\dfrac{196}{5}\right)\sqrt{7}-\dfrac{497}{4}\right)\left(\left(-\dfrac{69}{2}\right)\sqrt{7}\right)\\
&=&\left(-\dfrac{6762}{5}\right)\sqrt{49}+\left(\dfrac{34293}{8}\right)\sqrt{7}\\
&=&-\dfrac{47334}{5}+\left(\dfrac{34293}{8}\right)\sqrt{7}\\
\end{eqnarray*}