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 \( X=-7-\dfrac{8}{5}-\left(\left(\dfrac{69}{7}\right)\sqrt{63}-\dfrac{59}{5}\right)\) et \( Y=\left(-\dfrac{37}{3}\right)\sqrt{28}\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(-7-\dfrac{8}{5}-\left(\left(\dfrac{69}{7}\right)\sqrt{63}-\dfrac{59}{5}\right)\right)+\left(\left(-\dfrac{37}{3}\right)\sqrt{28}\right)\\
&=&\left(-7-\dfrac{8}{5}-\left(\left(\dfrac{207}{7}\right)\sqrt{7}-\dfrac{59}{5}\right)\right)+\left(\left(-\dfrac{74}{3}\right)\sqrt{7}\right)\\
&=&-7-\dfrac{8}{5}-\left(\left(\dfrac{207}{7}\right)\sqrt{7}-\dfrac{59}{5}\right)+\left(-\dfrac{74}{3}\right)\sqrt{7}\\
&=&\dfrac{16}{5}+\left(-\dfrac{1139}{21}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(-7-\dfrac{8}{5}-\left(\left(\dfrac{69}{7}\right)\sqrt{63}-\dfrac{59}{5}\right)\right)-\left(\left(-\dfrac{37}{3}\right)\sqrt{28}\right)\\
&=&\left(-7-\dfrac{8}{5}-\left(\left(\dfrac{207}{7}\right)\sqrt{7}-\dfrac{59}{5}\right)\right)-\left(\left(-\dfrac{74}{3}\right)\sqrt{7}\right)\\
&=&\left(\dfrac{16}{5}+\left(-\dfrac{207}{7}\right)\sqrt{7}\right)-\left(\left(-\dfrac{74}{3}\right)\sqrt{7}\right)\\
&=&\dfrac{16}{5}+\left(-\dfrac{207}{7}\right)\sqrt{7}+\left(\dfrac{74}{3}\right)\sqrt{7}\\
&=&\dfrac{16}{5}+\left(-\dfrac{103}{21}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(-7-\dfrac{8}{5}-\left(\left(\dfrac{69}{7}\right)\sqrt{63}-\dfrac{59}{5}\right)\right)\times\left(\left(-\dfrac{37}{3}\right)\sqrt{28}\right)\\
&=&\left(-7-\dfrac{8}{5}-\left(\left(\dfrac{207}{7}\right)\sqrt{7}-\dfrac{59}{5}\right)\right)\times\left(\left(-\dfrac{74}{3}\right)\sqrt{7}\right)\\
&=&\left(\dfrac{16}{5}+\left(-\dfrac{207}{7}\right)\sqrt{7}\right)\left(\left(-\dfrac{74}{3}\right)\sqrt{7}\right)\\
&=&\left(-\dfrac{1184}{15}\right)\sqrt{7}+\left(\dfrac{5106}{7}\right)\sqrt{49}\\
&=&\left(-\dfrac{1184}{15}\right)\sqrt{7}+5106\\
\end{eqnarray*}