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 \( X=\left(-\dfrac{6}{5}\right)\sqrt{175}\) et \( Y=\left(\left(-\dfrac{67}{6}\right)\sqrt{63}-\dfrac{24}{5}+\left(-\dfrac{61}{3}\right)\sqrt{49}+\left(\dfrac{79}{2}\right)\sqrt{63}\right)-\dfrac{11}{7}\) . 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{6}{5}\right)\sqrt{175}\right)+\left(\left(\left(-\dfrac{67}{6}\right)\sqrt{63}-\dfrac{24}{5}+\left(-\dfrac{61}{3}\right)\sqrt{49}+\left(\dfrac{79}{2}\right)\sqrt{63}\right)-\dfrac{11}{7}\right)\\
&=&\left(\left(-6\right)\sqrt{7}\right)+\left(\left(\left(-\dfrac{67}{2}\right)\sqrt{7}-\dfrac{24}{5}-\dfrac{427}{3}+\left(\dfrac{237}{2}\right)\sqrt{7}\right)-\dfrac{11}{7}\right)\\
&=&\left(-6\right)\sqrt{7}+\left(\left(-\dfrac{67}{2}\right)\sqrt{7}-\dfrac{24}{5}-\dfrac{427}{3}+\left(\dfrac{237}{2}\right)\sqrt{7}\right)-\dfrac{11}{7}\\
&=&\left(79\right)\sqrt{7}-\dfrac{15614}{105}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{6}{5}\right)\sqrt{175}\right)-\left(\left(\left(-\dfrac{67}{6}\right)\sqrt{63}-\dfrac{24}{5}+\left(-\dfrac{61}{3}\right)\sqrt{49}+\left(\dfrac{79}{2}\right)\sqrt{63}\right)-\dfrac{11}{7}\right)\\
&=&\left(\left(-6\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{67}{2}\right)\sqrt{7}-\dfrac{24}{5}-\dfrac{427}{3}+\left(\dfrac{237}{2}\right)\sqrt{7}\right)-\dfrac{11}{7}\right)\\
&=&\left(\left(-6\right)\sqrt{7}\right)-\left(\left(85\right)\sqrt{7}-\dfrac{15614}{105}\right)\\
&=&\left(-6\right)\sqrt{7}+\left(-85\right)\sqrt{7}+\dfrac{15614}{105}\\
&=&\left(-91\right)\sqrt{7}+\dfrac{15614}{105}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{6}{5}\right)\sqrt{175}\right)\times\left(\left(\left(-\dfrac{67}{6}\right)\sqrt{63}-\dfrac{24}{5}+\left(-\dfrac{61}{3}\right)\sqrt{49}+\left(\dfrac{79}{2}\right)\sqrt{63}\right)-\dfrac{11}{7}\right)\\
&=&\left(\left(-6\right)\sqrt{7}\right)\times\left(\left(\left(-\dfrac{67}{2}\right)\sqrt{7}-\dfrac{24}{5}-\dfrac{427}{3}+\left(\dfrac{237}{2}\right)\sqrt{7}\right)-\dfrac{11}{7}\right)\\
&=&\left(\left(-6\right)\sqrt{7}\right)\left(\left(85\right)\sqrt{7}-\dfrac{15614}{105}\right)\\
&=&\left(-510\right)\sqrt{49}+\left(\dfrac{31228}{35}\right)\sqrt{7}\\
&=&-3570+\left(\dfrac{31228}{35}\right)\sqrt{7}\\
\end{eqnarray*}