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 \( X=\left(\dfrac{16}{7}\right)\sqrt{63}\) et \( Y=\left(\left(4\right)\sqrt{49}+\left(\dfrac{81}{4}\right)\sqrt{63}+\left(0\right)\sqrt{63}+\left(\dfrac{23}{3}\right)\sqrt{49}\right)-\left(\left(-\dfrac{29}{7}\right)\sqrt{49}\right)-\left(\left(-\dfrac{2}{5}\right)\sqrt{49}+\left(\dfrac{67}{5}\right)\sqrt{28}+\left(-\dfrac{64}{9}\right)\sqrt{28}\right)-\left(\left(\left(-5\right)\sqrt{49}\right)-\left(\left(8\right)\sqrt{175}\right)-\left(\left(\dfrac{32}{9}\right)\sqrt{28}\right)-\left(\left(-\dfrac{56}{9}\right)\sqrt{175}\right)\right)\) . 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{16}{7}\right)\sqrt{63}\right)+\left(\left(\left(4\right)\sqrt{49}+\left(\dfrac{81}{4}\right)\sqrt{63}+\left(0\right)\sqrt{63}+\left(\dfrac{23}{3}\right)\sqrt{49}\right)-\left(\left(-\dfrac{29}{7}\right)\sqrt{49}\right)-\left(\left(-\dfrac{2}{5}\right)\sqrt{49}+\left(\dfrac{67}{5}\right)\sqrt{28}+\left(-\dfrac{64}{9}\right)\sqrt{28}\right)-\left(\left(\left(-5\right)\sqrt{49}\right)-\left(\left(8\right)\sqrt{175}\right)-\left(\left(\dfrac{32}{9}\right)\sqrt{28}\right)-\left(\left(-\dfrac{56}{9}\right)\sqrt{175}\right)\right)\right)\\
&=&\left(\left(\dfrac{48}{7}\right)\sqrt{7}\right)+\left(\left(28+\left(\dfrac{243}{4}\right)\sqrt{7}+\left(0\right)\sqrt{7}+\dfrac{161}{3}\right)+29-\left(-\dfrac{14}{5}+\left(\dfrac{134}{5}\right)\sqrt{7}+\left(-\dfrac{128}{9}\right)\sqrt{7}\right)-\left(-35-\left(\left(40\right)\sqrt{7}\right)-\left(\left(\dfrac{64}{9}\right)\sqrt{7}\right)-\left(\left(-\dfrac{280}{9}\right)\sqrt{7}\right)\right)\right)\\
&=&\left(\dfrac{48}{7}\right)\sqrt{7}+\left(28+\left(\dfrac{243}{4}\right)\sqrt{7}+\left(0\right)\sqrt{7}+\dfrac{161}{3}\right)+29-\left(-\dfrac{14}{5}+\left(\dfrac{134}{5}\right)\sqrt{7}+\left(-\dfrac{128}{9}\right)\sqrt{7}\right)-\left(-35-\left(\left(40\right)\sqrt{7}\right)-\left(\left(\dfrac{64}{9}\right)\sqrt{7}\right)-\left(\left(-\dfrac{280}{9}\right)\sqrt{7}\right)\right)\\
&=&\left(\dfrac{89497}{1260}\right)\sqrt{7}+\dfrac{2227}{15}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\dfrac{16}{7}\right)\sqrt{63}\right)-\left(\left(\left(4\right)\sqrt{49}+\left(\dfrac{81}{4}\right)\sqrt{63}+\left(0\right)\sqrt{63}+\left(\dfrac{23}{3}\right)\sqrt{49}\right)-\left(\left(-\dfrac{29}{7}\right)\sqrt{49}\right)-\left(\left(-\dfrac{2}{5}\right)\sqrt{49}+\left(\dfrac{67}{5}\right)\sqrt{28}+\left(-\dfrac{64}{9}\right)\sqrt{28}\right)-\left(\left(\left(-5\right)\sqrt{49}\right)-\left(\left(8\right)\sqrt{175}\right)-\left(\left(\dfrac{32}{9}\right)\sqrt{28}\right)-\left(\left(-\dfrac{56}{9}\right)\sqrt{175}\right)\right)\right)\\
&=&\left(\left(\dfrac{48}{7}\right)\sqrt{7}\right)-\left(\left(28+\left(\dfrac{243}{4}\right)\sqrt{7}+\left(0\right)\sqrt{7}+\dfrac{161}{3}\right)+29-\left(-\dfrac{14}{5}+\left(\dfrac{134}{5}\right)\sqrt{7}+\left(-\dfrac{128}{9}\right)\sqrt{7}\right)-\left(-35-\left(\left(40\right)\sqrt{7}\right)-\left(\left(\dfrac{64}{9}\right)\sqrt{7}\right)-\left(\left(-\dfrac{280}{9}\right)\sqrt{7}\right)\right)\right)\\
&=&\left(\left(\dfrac{48}{7}\right)\sqrt{7}\right)-\left(\dfrac{2227}{15}+\left(\dfrac{11551}{180}\right)\sqrt{7}\right)\\
&=&\left(\dfrac{48}{7}\right)\sqrt{7}+-\dfrac{2227}{15}+\left(-\dfrac{11551}{180}\right)\sqrt{7}\\
&=&\left(-\dfrac{72217}{1260}\right)\sqrt{7}-\dfrac{2227}{15}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\dfrac{16}{7}\right)\sqrt{63}\right)\times\left(\left(\left(4\right)\sqrt{49}+\left(\dfrac{81}{4}\right)\sqrt{63}+\left(0\right)\sqrt{63}+\left(\dfrac{23}{3}\right)\sqrt{49}\right)-\left(\left(-\dfrac{29}{7}\right)\sqrt{49}\right)-\left(\left(-\dfrac{2}{5}\right)\sqrt{49}+\left(\dfrac{67}{5}\right)\sqrt{28}+\left(-\dfrac{64}{9}\right)\sqrt{28}\right)-\left(\left(\left(-5\right)\sqrt{49}\right)-\left(\left(8\right)\sqrt{175}\right)-\left(\left(\dfrac{32}{9}\right)\sqrt{28}\right)-\left(\left(-\dfrac{56}{9}\right)\sqrt{175}\right)\right)\right)\\
&=&\left(\left(\dfrac{48}{7}\right)\sqrt{7}\right)\times\left(\left(28+\left(\dfrac{243}{4}\right)\sqrt{7}+\left(0\right)\sqrt{7}+\dfrac{161}{3}\right)+29-\left(-\dfrac{14}{5}+\left(\dfrac{134}{5}\right)\sqrt{7}+\left(-\dfrac{128}{9}\right)\sqrt{7}\right)-\left(-35-\left(\left(40\right)\sqrt{7}\right)-\left(\left(\dfrac{64}{9}\right)\sqrt{7}\right)-\left(\left(-\dfrac{280}{9}\right)\sqrt{7}\right)\right)\right)\\
&=&\left(\left(\dfrac{48}{7}\right)\sqrt{7}\right)\left(\dfrac{2227}{15}+\left(\dfrac{11551}{180}\right)\sqrt{7}\right)\\
&=&\left(\dfrac{35632}{35}\right)\sqrt{7}+\left(\dfrac{46204}{105}\right)\sqrt{49}\\
&=&\left(\dfrac{35632}{35}\right)\sqrt{7}+\dfrac{46204}{15}\\
\end{eqnarray*}