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 \( X=\left(\dfrac{5}{7}\right)\sqrt{49}\) et \( Y=\left(\left(-\dfrac{64}{5}\right)\sqrt{63}+\left(\dfrac{14}{9}\right)\sqrt{63}\right)-\left(\left(-\dfrac{17}{4}\right)\sqrt{49}\right)-\left(\left(\dfrac{81}{2}\right)\sqrt{63}+\left(-\dfrac{55}{9}\right)\sqrt{175}+9\right)-\left(\left(\left(-\dfrac{8}{7}\right)\sqrt{175}\right)-\left(\left(9\right)\sqrt{28}\right)-\left(\left(-8\right)\sqrt{28}\right)\right)\) . 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{5}{7}\right)\sqrt{49}\right)+\left(\left(\left(-\dfrac{64}{5}\right)\sqrt{63}+\left(\dfrac{14}{9}\right)\sqrt{63}\right)-\left(\left(-\dfrac{17}{4}\right)\sqrt{49}\right)-\left(\left(\dfrac{81}{2}\right)\sqrt{63}+\left(-\dfrac{55}{9}\right)\sqrt{175}+9\right)-\left(\left(\left(-\dfrac{8}{7}\right)\sqrt{175}\right)-\left(\left(9\right)\sqrt{28}\right)-\left(\left(-8\right)\sqrt{28}\right)\right)\right)\\
&=&\left(5\right)+\left(\left(\left(-\dfrac{192}{5}\right)\sqrt{7}+\left(\dfrac{14}{3}\right)\sqrt{7}\right)+\dfrac{119}{4}-\left(\left(\dfrac{243}{2}\right)\sqrt{7}+\left(-\dfrac{275}{9}\right)\sqrt{7}+9\right)-\left(\left(\left(-\dfrac{40}{7}\right)\sqrt{7}\right)-\left(\left(18\right)\sqrt{7}\right)-\left(\left(-16\right)\sqrt{7}\right)\right)\right)\\
&=&5+\left(\left(-\dfrac{192}{5}\right)\sqrt{7}+\left(\dfrac{14}{3}\right)\sqrt{7}\right)+\dfrac{119}{4}-\left(\left(\dfrac{243}{2}\right)\sqrt{7}+\left(-\dfrac{275}{9}\right)\sqrt{7}+9\right)-\left(\left(\left(-\dfrac{40}{7}\right)\sqrt{7}\right)-\left(\left(18\right)\sqrt{7}\right)-\left(\left(-16\right)\sqrt{7}\right)\right)\\
&=&\dfrac{103}{4}+\left(-\dfrac{73687}{630}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\dfrac{5}{7}\right)\sqrt{49}\right)-\left(\left(\left(-\dfrac{64}{5}\right)\sqrt{63}+\left(\dfrac{14}{9}\right)\sqrt{63}\right)-\left(\left(-\dfrac{17}{4}\right)\sqrt{49}\right)-\left(\left(\dfrac{81}{2}\right)\sqrt{63}+\left(-\dfrac{55}{9}\right)\sqrt{175}+9\right)-\left(\left(\left(-\dfrac{8}{7}\right)\sqrt{175}\right)-\left(\left(9\right)\sqrt{28}\right)-\left(\left(-8\right)\sqrt{28}\right)\right)\right)\\
&=&\left(5\right)-\left(\left(\left(-\dfrac{192}{5}\right)\sqrt{7}+\left(\dfrac{14}{3}\right)\sqrt{7}\right)+\dfrac{119}{4}-\left(\left(\dfrac{243}{2}\right)\sqrt{7}+\left(-\dfrac{275}{9}\right)\sqrt{7}+9\right)-\left(\left(\left(-\dfrac{40}{7}\right)\sqrt{7}\right)-\left(\left(18\right)\sqrt{7}\right)-\left(\left(-16\right)\sqrt{7}\right)\right)\right)\\
&=&\left(5\right)-\left(\left(-\dfrac{73687}{630}\right)\sqrt{7}+\dfrac{83}{4}\right)\\
&=&5+\left(\dfrac{73687}{630}\right)\sqrt{7}-\dfrac{83}{4}\\
&=&-\dfrac{63}{4}+\left(\dfrac{73687}{630}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\dfrac{5}{7}\right)\sqrt{49}\right)\times\left(\left(\left(-\dfrac{64}{5}\right)\sqrt{63}+\left(\dfrac{14}{9}\right)\sqrt{63}\right)-\left(\left(-\dfrac{17}{4}\right)\sqrt{49}\right)-\left(\left(\dfrac{81}{2}\right)\sqrt{63}+\left(-\dfrac{55}{9}\right)\sqrt{175}+9\right)-\left(\left(\left(-\dfrac{8}{7}\right)\sqrt{175}\right)-\left(\left(9\right)\sqrt{28}\right)-\left(\left(-8\right)\sqrt{28}\right)\right)\right)\\
&=&\left(5\right)\times\left(\left(\left(-\dfrac{192}{5}\right)\sqrt{7}+\left(\dfrac{14}{3}\right)\sqrt{7}\right)+\dfrac{119}{4}-\left(\left(\dfrac{243}{2}\right)\sqrt{7}+\left(-\dfrac{275}{9}\right)\sqrt{7}+9\right)-\left(\left(\left(-\dfrac{40}{7}\right)\sqrt{7}\right)-\left(\left(18\right)\sqrt{7}\right)-\left(\left(-16\right)\sqrt{7}\right)\right)\right)\\
&=&\left(5\right)\left(\left(-\dfrac{73687}{630}\right)\sqrt{7}+\dfrac{83}{4}\right)\\
&=&\left(-\dfrac{73687}{126}\right)\sqrt{7}+\dfrac{415}{4}\\
&=&\left(-\dfrac{73687}{126}\right)\sqrt{7}+\dfrac{415}{4}\\
\end{eqnarray*}