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 \( X=\left(\left(-7\right)\sqrt{9}\right)-\left(\left(\dfrac{40}{3}\right)\sqrt{9}\right)-\dfrac{43}{2}+\left(-\dfrac{57}{2}\right)\sqrt{27}+\left(\dfrac{35}{3}\right)\sqrt{75}-\dfrac{43}{2}+\left(4\right)\sqrt{75}+\left(-\dfrac{35}{4}\right)\sqrt{12}\) et \( Y=\left(\left(\dfrac{41}{6}\right)\sqrt{9}\right)-\left(\left(-\dfrac{29}{7}\right)\sqrt{12}\right)-4\) . 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(-7\right)\sqrt{9}\right)-\left(\left(\dfrac{40}{3}\right)\sqrt{9}\right)-\dfrac{43}{2}+\left(-\dfrac{57}{2}\right)\sqrt{27}+\left(\dfrac{35}{3}\right)\sqrt{75}-\dfrac{43}{2}+\left(4\right)\sqrt{75}+\left(-\dfrac{35}{4}\right)\sqrt{12}\right)+\left(\left(\left(\dfrac{41}{6}\right)\sqrt{9}\right)-\left(\left(-\dfrac{29}{7}\right)\sqrt{12}\right)-4\right)\\
&=&\left(-21-40-\dfrac{43}{2}+\left(-\dfrac{171}{2}\right)\sqrt{3}+\left(\dfrac{175}{3}\right)\sqrt{3}-\dfrac{43}{2}+\left(20\right)\sqrt{3}+\left(-\dfrac{35}{2}\right)\sqrt{3}\right)+\left(\dfrac{41}{2}-\left(\left(-\dfrac{58}{7}\right)\sqrt{3}\right)-4\right)\\
&=&-21-40-\dfrac{43}{2}+\left(-\dfrac{171}{2}\right)\sqrt{3}+\left(\dfrac{175}{3}\right)\sqrt{3}-\dfrac{43}{2}+\left(20\right)\sqrt{3}+\left(-\dfrac{35}{2}\right)\sqrt{3}+\dfrac{41}{2}-\left(\left(-\dfrac{58}{7}\right)\sqrt{3}\right)-4\\
&=&-\dfrac{175}{2}+\left(-\dfrac{344}{21}\right)\sqrt{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(-7\right)\sqrt{9}\right)-\left(\left(\dfrac{40}{3}\right)\sqrt{9}\right)-\dfrac{43}{2}+\left(-\dfrac{57}{2}\right)\sqrt{27}+\left(\dfrac{35}{3}\right)\sqrt{75}-\dfrac{43}{2}+\left(4\right)\sqrt{75}+\left(-\dfrac{35}{4}\right)\sqrt{12}\right)-\left(\left(\left(\dfrac{41}{6}\right)\sqrt{9}\right)-\left(\left(-\dfrac{29}{7}\right)\sqrt{12}\right)-4\right)\\
&=&\left(-21-40-\dfrac{43}{2}+\left(-\dfrac{171}{2}\right)\sqrt{3}+\left(\dfrac{175}{3}\right)\sqrt{3}-\dfrac{43}{2}+\left(20\right)\sqrt{3}+\left(-\dfrac{35}{2}\right)\sqrt{3}\right)-\left(\dfrac{41}{2}-\left(\left(-\dfrac{58}{7}\right)\sqrt{3}\right)-4\right)\\
&=&\left(-104+\left(-\dfrac{74}{3}\right)\sqrt{3}\right)-\left(\dfrac{33}{2}+\left(\dfrac{58}{7}\right)\sqrt{3}\right)\\
&=&-104+\left(-\dfrac{74}{3}\right)\sqrt{3}+-\dfrac{33}{2}+\left(-\dfrac{58}{7}\right)\sqrt{3}\\
&=&-\dfrac{241}{2}+\left(-\dfrac{692}{21}\right)\sqrt{3}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(-7\right)\sqrt{9}\right)-\left(\left(\dfrac{40}{3}\right)\sqrt{9}\right)-\dfrac{43}{2}+\left(-\dfrac{57}{2}\right)\sqrt{27}+\left(\dfrac{35}{3}\right)\sqrt{75}-\dfrac{43}{2}+\left(4\right)\sqrt{75}+\left(-\dfrac{35}{4}\right)\sqrt{12}\right)\times\left(\left(\left(\dfrac{41}{6}\right)\sqrt{9}\right)-\left(\left(-\dfrac{29}{7}\right)\sqrt{12}\right)-4\right)\\
&=&\left(-21-40-\dfrac{43}{2}+\left(-\dfrac{171}{2}\right)\sqrt{3}+\left(\dfrac{175}{3}\right)\sqrt{3}-\dfrac{43}{2}+\left(20\right)\sqrt{3}+\left(-\dfrac{35}{2}\right)\sqrt{3}\right)\times\left(\dfrac{41}{2}-\left(\left(-\dfrac{58}{7}\right)\sqrt{3}\right)-4\right)\\
&=&\left(-104+\left(-\dfrac{74}{3}\right)\sqrt{3}\right)\left(\dfrac{33}{2}+\left(\dfrac{58}{7}\right)\sqrt{3}\right)\\
&=&-1716+\left(-\dfrac{8881}{7}\right)\sqrt{3}+\left(-\dfrac{4292}{21}\right)\sqrt{9}\\
&=&-\dfrac{16304}{7}+\left(-\dfrac{8881}{7}\right)\sqrt{3}\\
\end{eqnarray*}