L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(\left(\left(\dfrac{7}{6}\right)\sqrt{175}\right)-\left(\left(9\right)\sqrt{49}\right)-\left(\left(\dfrac{50}{7}\right)\sqrt{63}\right)-\dfrac{3}{4}\right)-\left(\left(\left(-\dfrac{77}{9}\right)\sqrt{28}\right)-\left(\left(\dfrac{38}{9}\right)\sqrt{175}\right)\right)-\left(\left(\left(3\right)\sqrt{49}\right)+4-\left(\left(9\right)\sqrt{63}\right)\right)-\left(8+\left(1\right)\sqrt{49}+\left(\dfrac{61}{6}\right)\sqrt{28}+\left(2\right)\sqrt{63}\right)\) et \( Y=\left(-\dfrac{3}{8}\right)\sqrt{49}\) . 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(\left(\dfrac{7}{6}\right)\sqrt{175}\right)-\left(\left(9\right)\sqrt{49}\right)-\left(\left(\dfrac{50}{7}\right)\sqrt{63}\right)-\dfrac{3}{4}\right)-\left(\left(\left(-\dfrac{77}{9}\right)\sqrt{28}\right)-\left(\left(\dfrac{38}{9}\right)\sqrt{175}\right)\right)-\left(\left(\left(3\right)\sqrt{49}\right)+4-\left(\left(9\right)\sqrt{63}\right)\right)-\left(8+\left(1\right)\sqrt{49}+\left(\dfrac{61}{6}\right)\sqrt{28}+\left(2\right)\sqrt{63}\right)\right)+\left(\left(-\dfrac{3}{8}\right)\sqrt{49}\right)\\
&=&\left(\left(\left(\left(\dfrac{35}{6}\right)\sqrt{7}\right)-63-\left(\left(\dfrac{150}{7}\right)\sqrt{7}\right)-\dfrac{3}{4}\right)-\left(\left(\left(-\dfrac{154}{9}\right)\sqrt{7}\right)-\left(\left(\dfrac{190}{9}\right)\sqrt{7}\right)\right)-\left(21+4-\left(\left(27\right)\sqrt{7}\right)\right)-\left(8+7+\left(\dfrac{61}{3}\right)\sqrt{7}+\left(6\right)\sqrt{7}\right)\right)+\left(-\dfrac{21}{8}\right)\\
&=&\left(\left(\left(\dfrac{35}{6}\right)\sqrt{7}\right)-63-\left(\left(\dfrac{150}{7}\right)\sqrt{7}\right)-\dfrac{3}{4}\right)-\left(\left(\left(-\dfrac{154}{9}\right)\sqrt{7}\right)-\left(\left(\dfrac{190}{9}\right)\sqrt{7}\right)\right)-\left(21+4-\left(\left(27\right)\sqrt{7}\right)\right)-\left(8+7+\left(\dfrac{61}{3}\right)\sqrt{7}+\left(6\right)\sqrt{7}\right)-\dfrac{21}{8}\\
&=&\left(\dfrac{2935}{126}\right)\sqrt{7}-\dfrac{851}{8}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(\left(\dfrac{7}{6}\right)\sqrt{175}\right)-\left(\left(9\right)\sqrt{49}\right)-\left(\left(\dfrac{50}{7}\right)\sqrt{63}\right)-\dfrac{3}{4}\right)-\left(\left(\left(-\dfrac{77}{9}\right)\sqrt{28}\right)-\left(\left(\dfrac{38}{9}\right)\sqrt{175}\right)\right)-\left(\left(\left(3\right)\sqrt{49}\right)+4-\left(\left(9\right)\sqrt{63}\right)\right)-\left(8+\left(1\right)\sqrt{49}+\left(\dfrac{61}{6}\right)\sqrt{28}+\left(2\right)\sqrt{63}\right)\right)-\left(\left(-\dfrac{3}{8}\right)\sqrt{49}\right)\\
&=&\left(\left(\left(\left(\dfrac{35}{6}\right)\sqrt{7}\right)-63-\left(\left(\dfrac{150}{7}\right)\sqrt{7}\right)-\dfrac{3}{4}\right)-\left(\left(\left(-\dfrac{154}{9}\right)\sqrt{7}\right)-\left(\left(\dfrac{190}{9}\right)\sqrt{7}\right)\right)-\left(21+4-\left(\left(27\right)\sqrt{7}\right)\right)-\left(8+7+\left(\dfrac{61}{3}\right)\sqrt{7}+\left(6\right)\sqrt{7}\right)\right)-\left(-\dfrac{21}{8}\right)\\
&=&\left(\left(\dfrac{2935}{126}\right)\sqrt{7}-\dfrac{415}{4}\right)-\left(-\dfrac{21}{8}\right)\\
&=&\left(\dfrac{2935}{126}\right)\sqrt{7}-\dfrac{415}{4}+\dfrac{21}{8}\\
&=&\left(\dfrac{2935}{126}\right)\sqrt{7}-\dfrac{809}{8}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(\left(\dfrac{7}{6}\right)\sqrt{175}\right)-\left(\left(9\right)\sqrt{49}\right)-\left(\left(\dfrac{50}{7}\right)\sqrt{63}\right)-\dfrac{3}{4}\right)-\left(\left(\left(-\dfrac{77}{9}\right)\sqrt{28}\right)-\left(\left(\dfrac{38}{9}\right)\sqrt{175}\right)\right)-\left(\left(\left(3\right)\sqrt{49}\right)+4-\left(\left(9\right)\sqrt{63}\right)\right)-\left(8+\left(1\right)\sqrt{49}+\left(\dfrac{61}{6}\right)\sqrt{28}+\left(2\right)\sqrt{63}\right)\right)\times\left(\left(-\dfrac{3}{8}\right)\sqrt{49}\right)\\
&=&\left(\left(\left(\left(\dfrac{35}{6}\right)\sqrt{7}\right)-63-\left(\left(\dfrac{150}{7}\right)\sqrt{7}\right)-\dfrac{3}{4}\right)-\left(\left(\left(-\dfrac{154}{9}\right)\sqrt{7}\right)-\left(\left(\dfrac{190}{9}\right)\sqrt{7}\right)\right)-\left(21+4-\left(\left(27\right)\sqrt{7}\right)\right)-\left(8+7+\left(\dfrac{61}{3}\right)\sqrt{7}+\left(6\right)\sqrt{7}\right)\right)\times\left(-\dfrac{21}{8}\right)\\
&=&\left(\left(\dfrac{2935}{126}\right)\sqrt{7}-\dfrac{415}{4}\right)\left(-\dfrac{21}{8}\right)\\
&=&\left(-\dfrac{2935}{48}\right)\sqrt{7}+\dfrac{8715}{32}\\
&=&\left(-\dfrac{2935}{48}\right)\sqrt{7}+\dfrac{8715}{32}\\
\end{eqnarray*}