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 \( X=\left(-\dfrac{76}{5}\right)\sqrt{63}\) et \( Y=\left(\left(-8\right)\sqrt{28}\right)-\left(\left(\dfrac{37}{3}\right)\sqrt{175}\right)-5-\left(\left(-\dfrac{5}{6}\right)\sqrt{63}\right)-\left(\left(-7\right)\sqrt{28}\right)+\dfrac{1}{8}+\left(-6\right)\sqrt{28}+\left(-8\right)\sqrt{63}\) . 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{76}{5}\right)\sqrt{63}\right)+\left(\left(\left(-8\right)\sqrt{28}\right)-\left(\left(\dfrac{37}{3}\right)\sqrt{175}\right)-5-\left(\left(-\dfrac{5}{6}\right)\sqrt{63}\right)-\left(\left(-7\right)\sqrt{28}\right)+\dfrac{1}{8}+\left(-6\right)\sqrt{28}+\left(-8\right)\sqrt{63}\right)\\
&=&\left(\left(-\dfrac{228}{5}\right)\sqrt{7}\right)+\left(\left(\left(-16\right)\sqrt{7}\right)-\left(\left(\dfrac{185}{3}\right)\sqrt{7}\right)-5-\left(\left(-\dfrac{5}{2}\right)\sqrt{7}\right)-\left(\left(-14\right)\sqrt{7}\right)+\dfrac{1}{8}+\left(-12\right)\sqrt{7}+\left(-24\right)\sqrt{7}\right)\\
&=&\left(-\dfrac{228}{5}\right)\sqrt{7}+\left(\left(-16\right)\sqrt{7}\right)-\left(\left(\dfrac{185}{3}\right)\sqrt{7}\right)-5-\left(\left(-\dfrac{5}{2}\right)\sqrt{7}\right)-\left(\left(-14\right)\sqrt{7}\right)+\dfrac{1}{8}+\left(-12\right)\sqrt{7}+\left(-24\right)\sqrt{7}\\
&=&\left(-\dfrac{4283}{30}\right)\sqrt{7}-\dfrac{39}{8}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{76}{5}\right)\sqrt{63}\right)-\left(\left(\left(-8\right)\sqrt{28}\right)-\left(\left(\dfrac{37}{3}\right)\sqrt{175}\right)-5-\left(\left(-\dfrac{5}{6}\right)\sqrt{63}\right)-\left(\left(-7\right)\sqrt{28}\right)+\dfrac{1}{8}+\left(-6\right)\sqrt{28}+\left(-8\right)\sqrt{63}\right)\\
&=&\left(\left(-\dfrac{228}{5}\right)\sqrt{7}\right)-\left(\left(\left(-16\right)\sqrt{7}\right)-\left(\left(\dfrac{185}{3}\right)\sqrt{7}\right)-5-\left(\left(-\dfrac{5}{2}\right)\sqrt{7}\right)-\left(\left(-14\right)\sqrt{7}\right)+\dfrac{1}{8}+\left(-12\right)\sqrt{7}+\left(-24\right)\sqrt{7}\right)\\
&=&\left(\left(-\dfrac{228}{5}\right)\sqrt{7}\right)-\left(\left(-\dfrac{583}{6}\right)\sqrt{7}-\dfrac{39}{8}\right)\\
&=&\left(-\dfrac{228}{5}\right)\sqrt{7}+\left(\dfrac{583}{6}\right)\sqrt{7}+\dfrac{39}{8}\\
&=&\left(\dfrac{1547}{30}\right)\sqrt{7}+\dfrac{39}{8}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{76}{5}\right)\sqrt{63}\right)\times\left(\left(\left(-8\right)\sqrt{28}\right)-\left(\left(\dfrac{37}{3}\right)\sqrt{175}\right)-5-\left(\left(-\dfrac{5}{6}\right)\sqrt{63}\right)-\left(\left(-7\right)\sqrt{28}\right)+\dfrac{1}{8}+\left(-6\right)\sqrt{28}+\left(-8\right)\sqrt{63}\right)\\
&=&\left(\left(-\dfrac{228}{5}\right)\sqrt{7}\right)\times\left(\left(\left(-16\right)\sqrt{7}\right)-\left(\left(\dfrac{185}{3}\right)\sqrt{7}\right)-5-\left(\left(-\dfrac{5}{2}\right)\sqrt{7}\right)-\left(\left(-14\right)\sqrt{7}\right)+\dfrac{1}{8}+\left(-12\right)\sqrt{7}+\left(-24\right)\sqrt{7}\right)\\
&=&\left(\left(-\dfrac{228}{5}\right)\sqrt{7}\right)\left(\left(-\dfrac{583}{6}\right)\sqrt{7}-\dfrac{39}{8}\right)\\
&=&\left(\dfrac{22154}{5}\right)\sqrt{49}+\left(\dfrac{2223}{10}\right)\sqrt{7}\\
&=&\dfrac{155078}{5}+\left(\dfrac{2223}{10}\right)\sqrt{7}\\
\end{eqnarray*}