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 \( X=\left(\left(\dfrac{79}{4}\right)\sqrt{49}\right)-\left(\left(\left(9\right)\sqrt{49}\right)-8\right)\) et \( Y=\left(-\dfrac{44}{3}-\left(\left(-\dfrac{59}{2}\right)\sqrt{28}\right)-\left(\left(-\dfrac{3}{4}\right)\sqrt{49}\right)\right)-\left(\left(1\right)\sqrt{175}+\left(\dfrac{17}{7}\right)\sqrt{63}-\dfrac{46}{7}\right)-\left(\left(-\dfrac{29}{9}\right)\sqrt{49}\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(\left(\dfrac{79}{4}\right)\sqrt{49}\right)-\left(\left(\left(9\right)\sqrt{49}\right)-8\right)\right)+\left(\left(-\dfrac{44}{3}-\left(\left(-\dfrac{59}{2}\right)\sqrt{28}\right)-\left(\left(-\dfrac{3}{4}\right)\sqrt{49}\right)\right)-\left(\left(1\right)\sqrt{175}+\left(\dfrac{17}{7}\right)\sqrt{63}-\dfrac{46}{7}\right)-\left(\left(-\dfrac{29}{9}\right)\sqrt{49}\right)\right)\\
&=&\left(\dfrac{553}{4}-\left(63-8\right)\right)+\left(\left(-\dfrac{44}{3}-\left(\left(-59\right)\sqrt{7}\right)+\dfrac{21}{4}\right)-\left(\left(5\right)\sqrt{7}+\left(\dfrac{51}{7}\right)\sqrt{7}-\dfrac{46}{7}\right)+\dfrac{203}{9}\right)\\
&=&\dfrac{553}{4}-\left(63-8\right)+\left(-\dfrac{44}{3}-\left(\left(-59\right)\sqrt{7}\right)+\dfrac{21}{4}\right)-\left(\left(5\right)\sqrt{7}+\left(\dfrac{51}{7}\right)\sqrt{7}-\dfrac{46}{7}\right)+\dfrac{203}{9}\\
&=&\dfrac{12973}{126}+\left(\dfrac{327}{7}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(\dfrac{79}{4}\right)\sqrt{49}\right)-\left(\left(\left(9\right)\sqrt{49}\right)-8\right)\right)-\left(\left(-\dfrac{44}{3}-\left(\left(-\dfrac{59}{2}\right)\sqrt{28}\right)-\left(\left(-\dfrac{3}{4}\right)\sqrt{49}\right)\right)-\left(\left(1\right)\sqrt{175}+\left(\dfrac{17}{7}\right)\sqrt{63}-\dfrac{46}{7}\right)-\left(\left(-\dfrac{29}{9}\right)\sqrt{49}\right)\right)\\
&=&\left(\dfrac{553}{4}-\left(63-8\right)\right)-\left(\left(-\dfrac{44}{3}-\left(\left(-59\right)\sqrt{7}\right)+\dfrac{21}{4}\right)-\left(\left(5\right)\sqrt{7}+\left(\dfrac{51}{7}\right)\sqrt{7}-\dfrac{46}{7}\right)+\dfrac{203}{9}\right)\\
&=&\left(\dfrac{333}{4}\right)-\left(\dfrac{4967}{252}+\left(\dfrac{327}{7}\right)\sqrt{7}\right)\\
&=&\dfrac{333}{4}+-\dfrac{4967}{252}+\left(-\dfrac{327}{7}\right)\sqrt{7}\\
&=&\dfrac{4003}{63}+\left(-\dfrac{327}{7}\right)\sqrt{7}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(\dfrac{79}{4}\right)\sqrt{49}\right)-\left(\left(\left(9\right)\sqrt{49}\right)-8\right)\right)\times\left(\left(-\dfrac{44}{3}-\left(\left(-\dfrac{59}{2}\right)\sqrt{28}\right)-\left(\left(-\dfrac{3}{4}\right)\sqrt{49}\right)\right)-\left(\left(1\right)\sqrt{175}+\left(\dfrac{17}{7}\right)\sqrt{63}-\dfrac{46}{7}\right)-\left(\left(-\dfrac{29}{9}\right)\sqrt{49}\right)\right)\\
&=&\left(\dfrac{553}{4}-\left(63-8\right)\right)\times\left(\left(-\dfrac{44}{3}-\left(\left(-59\right)\sqrt{7}\right)+\dfrac{21}{4}\right)-\left(\left(5\right)\sqrt{7}+\left(\dfrac{51}{7}\right)\sqrt{7}-\dfrac{46}{7}\right)+\dfrac{203}{9}\right)\\
&=&\left(\dfrac{333}{4}\right)\left(\dfrac{4967}{252}+\left(\dfrac{327}{7}\right)\sqrt{7}\right)\\
&=&\dfrac{183779}{112}+\left(\dfrac{108891}{28}\right)\sqrt{7}\\
&=&\dfrac{183779}{112}+\left(\dfrac{108891}{28}\right)\sqrt{7}\\
\end{eqnarray*}