L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Soit \( X=\left(8\right)\sqrt{63}\) et \( Y=\left(\left(\left(\dfrac{2}{5}\right)\sqrt{63}\right)-\left(\left(-\dfrac{53}{2}\right)\sqrt{63}\right)-\left(\left(3\right)\sqrt{28}\right)-\left(\left(-\dfrac{79}{8}\right)\sqrt{63}\right)\right)-\left(\dfrac{59}{9}+2+\dfrac{17}{2}-\left(\left(-\dfrac{41}{4}\right)\sqrt{49}\right)\right)-\left(\left(\left(0\right)\sqrt{49}\right)-\left(\left(-\dfrac{11}{2}\right)\sqrt{49}\right)\right)-\left(\left(\left(-9\right)\sqrt{175}\right)+2+\dfrac{33}{4}-\left(\left(-\dfrac{50}{9}\right)\sqrt{175}\right)-\left(\left(0\right)\sqrt{175}\right)\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(8\right)\sqrt{63}\right)+\left(\left(\left(\left(\dfrac{2}{5}\right)\sqrt{63}\right)-\left(\left(-\dfrac{53}{2}\right)\sqrt{63}\right)-\left(\left(3\right)\sqrt{28}\right)-\left(\left(-\dfrac{79}{8}\right)\sqrt{63}\right)\right)-\left(\dfrac{59}{9}+2+\dfrac{17}{2}-\left(\left(-\dfrac{41}{4}\right)\sqrt{49}\right)\right)-\left(\left(\left(0\right)\sqrt{49}\right)-\left(\left(-\dfrac{11}{2}\right)\sqrt{49}\right)\right)-\left(\left(\left(-9\right)\sqrt{175}\right)+2+\dfrac{33}{4}-\left(\left(-\dfrac{50}{9}\right)\sqrt{175}\right)-\left(\left(0\right)\sqrt{175}\right)\right)\right)\\
&=&\left(\left(24\right)\sqrt{7}\right)+\left(\left(\left(\left(\dfrac{6}{5}\right)\sqrt{7}\right)-\left(\left(-\dfrac{159}{2}\right)\sqrt{7}\right)-\left(\left(6\right)\sqrt{7}\right)-\left(\left(-\dfrac{237}{8}\right)\sqrt{7}\right)\right)-\left(\dfrac{59}{9}+2+\dfrac{17}{2}+\dfrac{287}{4}\right)-\left(0+\dfrac{77}{2}\right)-\left(\left(\left(-45\right)\sqrt{7}\right)+2+\dfrac{33}{4}-\left(\left(-\dfrac{250}{9}\right)\sqrt{7}\right)-\left(\left(0\right)\sqrt{7}\right)\right)\right)\\
&=&\left(24\right)\sqrt{7}+\left(\left(\left(\dfrac{6}{5}\right)\sqrt{7}\right)-\left(\left(-\dfrac{159}{2}\right)\sqrt{7}\right)-\left(\left(6\right)\sqrt{7}\right)-\left(\left(-\dfrac{237}{8}\right)\sqrt{7}\right)\right)-\left(\dfrac{59}{9}+2+\dfrac{17}{2}+\dfrac{287}{4}\right)-\left(0+\dfrac{77}{2}\right)-\left(\left(\left(-45\right)\sqrt{7}\right)+2+\dfrac{33}{4}-\left(\left(-\dfrac{250}{9}\right)\sqrt{7}\right)-\left(\left(0\right)\sqrt{7}\right)\right)\\
&=&\left(\dfrac{52397}{360}\right)\sqrt{7}-\dfrac{1238}{9}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(8\right)\sqrt{63}\right)-\left(\left(\left(\left(\dfrac{2}{5}\right)\sqrt{63}\right)-\left(\left(-\dfrac{53}{2}\right)\sqrt{63}\right)-\left(\left(3\right)\sqrt{28}\right)-\left(\left(-\dfrac{79}{8}\right)\sqrt{63}\right)\right)-\left(\dfrac{59}{9}+2+\dfrac{17}{2}-\left(\left(-\dfrac{41}{4}\right)\sqrt{49}\right)\right)-\left(\left(\left(0\right)\sqrt{49}\right)-\left(\left(-\dfrac{11}{2}\right)\sqrt{49}\right)\right)-\left(\left(\left(-9\right)\sqrt{175}\right)+2+\dfrac{33}{4}-\left(\left(-\dfrac{50}{9}\right)\sqrt{175}\right)-\left(\left(0\right)\sqrt{175}\right)\right)\right)\\
&=&\left(\left(24\right)\sqrt{7}\right)-\left(\left(\left(\left(\dfrac{6}{5}\right)\sqrt{7}\right)-\left(\left(-\dfrac{159}{2}\right)\sqrt{7}\right)-\left(\left(6\right)\sqrt{7}\right)-\left(\left(-\dfrac{237}{8}\right)\sqrt{7}\right)\right)-\left(\dfrac{59}{9}+2+\dfrac{17}{2}+\dfrac{287}{4}\right)-\left(0+\dfrac{77}{2}\right)-\left(\left(\left(-45\right)\sqrt{7}\right)+2+\dfrac{33}{4}-\left(\left(-\dfrac{250}{9}\right)\sqrt{7}\right)-\left(\left(0\right)\sqrt{7}\right)\right)\right)\\
&=&\left(\left(24\right)\sqrt{7}\right)-\left(\left(\dfrac{43757}{360}\right)\sqrt{7}-\dfrac{1238}{9}\right)\\
&=&\left(24\right)\sqrt{7}+\left(-\dfrac{43757}{360}\right)\sqrt{7}+\dfrac{1238}{9}\\
&=&\left(-\dfrac{35117}{360}\right)\sqrt{7}+\dfrac{1238}{9}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(8\right)\sqrt{63}\right)\times\left(\left(\left(\left(\dfrac{2}{5}\right)\sqrt{63}\right)-\left(\left(-\dfrac{53}{2}\right)\sqrt{63}\right)-\left(\left(3\right)\sqrt{28}\right)-\left(\left(-\dfrac{79}{8}\right)\sqrt{63}\right)\right)-\left(\dfrac{59}{9}+2+\dfrac{17}{2}-\left(\left(-\dfrac{41}{4}\right)\sqrt{49}\right)\right)-\left(\left(\left(0\right)\sqrt{49}\right)-\left(\left(-\dfrac{11}{2}\right)\sqrt{49}\right)\right)-\left(\left(\left(-9\right)\sqrt{175}\right)+2+\dfrac{33}{4}-\left(\left(-\dfrac{50}{9}\right)\sqrt{175}\right)-\left(\left(0\right)\sqrt{175}\right)\right)\right)\\
&=&\left(\left(24\right)\sqrt{7}\right)\times\left(\left(\left(\left(\dfrac{6}{5}\right)\sqrt{7}\right)-\left(\left(-\dfrac{159}{2}\right)\sqrt{7}\right)-\left(\left(6\right)\sqrt{7}\right)-\left(\left(-\dfrac{237}{8}\right)\sqrt{7}\right)\right)-\left(\dfrac{59}{9}+2+\dfrac{17}{2}+\dfrac{287}{4}\right)-\left(0+\dfrac{77}{2}\right)-\left(\left(\left(-45\right)\sqrt{7}\right)+2+\dfrac{33}{4}-\left(\left(-\dfrac{250}{9}\right)\sqrt{7}\right)-\left(\left(0\right)\sqrt{7}\right)\right)\right)\\
&=&\left(\left(24\right)\sqrt{7}\right)\left(\left(\dfrac{43757}{360}\right)\sqrt{7}-\dfrac{1238}{9}\right)\\
&=&\left(\dfrac{43757}{15}\right)\sqrt{49}+\left(-\dfrac{9904}{3}\right)\sqrt{7}\\
&=&\dfrac{306299}{15}+\left(-\dfrac{9904}{3}\right)\sqrt{7}\\
\end{eqnarray*}