L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(\left(-3\right)\sqrt{28}\right)-\left(0-\left(\left(2\right)\sqrt{49}\right)-\left(\left(2\right)\sqrt{49}\right)\right)-\left(\left(\dfrac{63}{8}\right)\sqrt{63}-\dfrac{11}{3}\right)\) et \( Y=\left(\left(-\dfrac{25}{8}\right)\sqrt{175}\right)-\left(\dfrac{78}{5}-\left(\left(\dfrac{23}{3}\right)\sqrt{63}\right)-7-\left(\left(\dfrac{32}{3}\right)\sqrt{28}\right)\right)-\left(\left(\left(\dfrac{32}{3}\right)\sqrt{28}\right)-0-\left(\left(-\dfrac{43}{6}\right)\sqrt{175}\right)-\left(\left(\dfrac{32}{3}\right)\sqrt{28}\right)\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(\left(-3\right)\sqrt{28}\right)-\left(0-\left(\left(2\right)\sqrt{49}\right)-\left(\left(2\right)\sqrt{49}\right)\right)-\left(\left(\dfrac{63}{8}\right)\sqrt{63}-\dfrac{11}{3}\right)\right)+\left(\left(\left(-\dfrac{25}{8}\right)\sqrt{175}\right)-\left(\dfrac{78}{5}-\left(\left(\dfrac{23}{3}\right)\sqrt{63}\right)-7-\left(\left(\dfrac{32}{3}\right)\sqrt{28}\right)\right)-\left(\left(\left(\dfrac{32}{3}\right)\sqrt{28}\right)-0-\left(\left(-\dfrac{43}{6}\right)\sqrt{175}\right)-\left(\left(\dfrac{32}{3}\right)\sqrt{28}\right)\right)\right)\\
&=&\left(\left(\left(-6\right)\sqrt{7}\right)-\left(0-14-14\right)-\left(\left(\dfrac{189}{8}\right)\sqrt{7}-\dfrac{11}{3}\right)\right)+\left(\left(\left(-\dfrac{125}{8}\right)\sqrt{7}\right)-\left(\dfrac{78}{5}-\left(\left(23\right)\sqrt{7}\right)-7-\left(\left(\dfrac{64}{3}\right)\sqrt{7}\right)\right)-\left(\left(\left(\dfrac{64}{3}\right)\sqrt{7}\right)-0-\left(\left(-\dfrac{215}{6}\right)\sqrt{7}\right)-\left(\left(\dfrac{64}{3}\right)\sqrt{7}\right)\right)\right)\\
&=&\left(\left(-6\right)\sqrt{7}\right)-\left(0-14-14\right)-\left(\left(\dfrac{189}{8}\right)\sqrt{7}-\dfrac{11}{3}\right)+\left(\left(-\dfrac{125}{8}\right)\sqrt{7}\right)-\left(\dfrac{78}{5}-\left(\left(23\right)\sqrt{7}\right)-7-\left(\left(\dfrac{64}{3}\right)\sqrt{7}\right)\right)-\left(\left(\left(\dfrac{64}{3}\right)\sqrt{7}\right)-0-\left(\left(-\dfrac{215}{6}\right)\sqrt{7}\right)-\left(\left(\dfrac{64}{3}\right)\sqrt{7}\right)\right)\\
&=&\left(-\dfrac{147}{4}\right)\sqrt{7}+\dfrac{346}{15}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(-3\right)\sqrt{28}\right)-\left(0-\left(\left(2\right)\sqrt{49}\right)-\left(\left(2\right)\sqrt{49}\right)\right)-\left(\left(\dfrac{63}{8}\right)\sqrt{63}-\dfrac{11}{3}\right)\right)-\left(\left(\left(-\dfrac{25}{8}\right)\sqrt{175}\right)-\left(\dfrac{78}{5}-\left(\left(\dfrac{23}{3}\right)\sqrt{63}\right)-7-\left(\left(\dfrac{32}{3}\right)\sqrt{28}\right)\right)-\left(\left(\left(\dfrac{32}{3}\right)\sqrt{28}\right)-0-\left(\left(-\dfrac{43}{6}\right)\sqrt{175}\right)-\left(\left(\dfrac{32}{3}\right)\sqrt{28}\right)\right)\right)\\
&=&\left(\left(\left(-6\right)\sqrt{7}\right)-\left(0-14-14\right)-\left(\left(\dfrac{189}{8}\right)\sqrt{7}-\dfrac{11}{3}\right)\right)-\left(\left(\left(-\dfrac{125}{8}\right)\sqrt{7}\right)-\left(\dfrac{78}{5}-\left(\left(23\right)\sqrt{7}\right)-7-\left(\left(\dfrac{64}{3}\right)\sqrt{7}\right)\right)-\left(\left(\left(\dfrac{64}{3}\right)\sqrt{7}\right)-0-\left(\left(-\dfrac{215}{6}\right)\sqrt{7}\right)-\left(\left(\dfrac{64}{3}\right)\sqrt{7}\right)\right)\right)\\
&=&\left(\left(-\dfrac{237}{8}\right)\sqrt{7}+\dfrac{95}{3}\right)-\left(\left(-\dfrac{57}{8}\right)\sqrt{7}-\dfrac{43}{5}\right)\\
&=&\left(-\dfrac{237}{8}\right)\sqrt{7}+\dfrac{95}{3}+\left(\dfrac{57}{8}\right)\sqrt{7}+\dfrac{43}{5}\\
&=&\left(-\dfrac{45}{2}\right)\sqrt{7}+\dfrac{604}{15}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(-3\right)\sqrt{28}\right)-\left(0-\left(\left(2\right)\sqrt{49}\right)-\left(\left(2\right)\sqrt{49}\right)\right)-\left(\left(\dfrac{63}{8}\right)\sqrt{63}-\dfrac{11}{3}\right)\right)\times\left(\left(\left(-\dfrac{25}{8}\right)\sqrt{175}\right)-\left(\dfrac{78}{5}-\left(\left(\dfrac{23}{3}\right)\sqrt{63}\right)-7-\left(\left(\dfrac{32}{3}\right)\sqrt{28}\right)\right)-\left(\left(\left(\dfrac{32}{3}\right)\sqrt{28}\right)-0-\left(\left(-\dfrac{43}{6}\right)\sqrt{175}\right)-\left(\left(\dfrac{32}{3}\right)\sqrt{28}\right)\right)\right)\\
&=&\left(\left(\left(-6\right)\sqrt{7}\right)-\left(0-14-14\right)-\left(\left(\dfrac{189}{8}\right)\sqrt{7}-\dfrac{11}{3}\right)\right)\times\left(\left(\left(-\dfrac{125}{8}\right)\sqrt{7}\right)-\left(\dfrac{78}{5}-\left(\left(23\right)\sqrt{7}\right)-7-\left(\left(\dfrac{64}{3}\right)\sqrt{7}\right)\right)-\left(\left(\left(\dfrac{64}{3}\right)\sqrt{7}\right)-0-\left(\left(-\dfrac{215}{6}\right)\sqrt{7}\right)-\left(\left(\dfrac{64}{3}\right)\sqrt{7}\right)\right)\right)\\
&=&\left(\left(-\dfrac{237}{8}\right)\sqrt{7}+\dfrac{95}{3}\right)\left(\left(-\dfrac{57}{8}\right)\sqrt{7}-\dfrac{43}{5}\right)\\
&=&\left(\dfrac{13509}{64}\right)\sqrt{49}+\left(\dfrac{583}{20}\right)\sqrt{7}-\dfrac{817}{3}\\
&=&\dfrac{231401}{192}+\left(\dfrac{583}{20}\right)\sqrt{7}\\
\end{eqnarray*}