L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Soit \( X=\left(-\dfrac{29}{6}\right)\sqrt{28}+\left(0\right)\sqrt{28}+\dfrac{57}{8}-5-\left(\left(\dfrac{9}{4}\right)\sqrt{49}\right)\) et \( Y=\left(\left(-\dfrac{47}{4}\right)\sqrt{63}+\left(\dfrac{19}{2}\right)\sqrt{28}\right)-\left(\left(\left(-\dfrac{19}{2}\right)\sqrt{175}\right)-\left(\left(\dfrac{66}{5}\right)\sqrt{63}\right)-\left(\left(-\dfrac{19}{3}\right)\sqrt{28}\right)\right)-\left(\left(\left(-\dfrac{2}{7}\right)\sqrt{49}\right)+\dfrac{13}{4}\right)-2\) . 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{29}{6}\right)\sqrt{28}+\left(0\right)\sqrt{28}+\dfrac{57}{8}-5-\left(\left(\dfrac{9}{4}\right)\sqrt{49}\right)\right)+\left(\left(\left(-\dfrac{47}{4}\right)\sqrt{63}+\left(\dfrac{19}{2}\right)\sqrt{28}\right)-\left(\left(\left(-\dfrac{19}{2}\right)\sqrt{175}\right)-\left(\left(\dfrac{66}{5}\right)\sqrt{63}\right)-\left(\left(-\dfrac{19}{3}\right)\sqrt{28}\right)\right)-\left(\left(\left(-\dfrac{2}{7}\right)\sqrt{49}\right)+\dfrac{13}{4}\right)-2\right)\\
&=&\left(\left(-\dfrac{29}{3}\right)\sqrt{7}+\left(0\right)\sqrt{7}+\dfrac{57}{8}-5-\dfrac{63}{4}\right)+\left(\left(\left(-\dfrac{141}{4}\right)\sqrt{7}+\left(19\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{95}{2}\right)\sqrt{7}\right)-\left(\left(\dfrac{198}{5}\right)\sqrt{7}\right)-\left(\left(-\dfrac{38}{3}\right)\sqrt{7}\right)\right)-\left(-2+\dfrac{13}{4}\right)-2\right)\\
&=&\left(-\dfrac{29}{3}\right)\sqrt{7}+\left(0\right)\sqrt{7}+\dfrac{57}{8}-5-\dfrac{63}{4}+\left(\left(-\dfrac{141}{4}\right)\sqrt{7}+\left(19\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{95}{2}\right)\sqrt{7}\right)-\left(\left(\dfrac{198}{5}\right)\sqrt{7}\right)-\left(\left(-\dfrac{38}{3}\right)\sqrt{7}\right)\right)-\left(-2+\dfrac{13}{4}\right)-2\\
&=&\left(\dfrac{2911}{60}\right)\sqrt{7}-\dfrac{135}{8}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{29}{6}\right)\sqrt{28}+\left(0\right)\sqrt{28}+\dfrac{57}{8}-5-\left(\left(\dfrac{9}{4}\right)\sqrt{49}\right)\right)-\left(\left(\left(-\dfrac{47}{4}\right)\sqrt{63}+\left(\dfrac{19}{2}\right)\sqrt{28}\right)-\left(\left(\left(-\dfrac{19}{2}\right)\sqrt{175}\right)-\left(\left(\dfrac{66}{5}\right)\sqrt{63}\right)-\left(\left(-\dfrac{19}{3}\right)\sqrt{28}\right)\right)-\left(\left(\left(-\dfrac{2}{7}\right)\sqrt{49}\right)+\dfrac{13}{4}\right)-2\right)\\
&=&\left(\left(-\dfrac{29}{3}\right)\sqrt{7}+\left(0\right)\sqrt{7}+\dfrac{57}{8}-5-\dfrac{63}{4}\right)-\left(\left(\left(-\dfrac{141}{4}\right)\sqrt{7}+\left(19\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{95}{2}\right)\sqrt{7}\right)-\left(\left(\dfrac{198}{5}\right)\sqrt{7}\right)-\left(\left(-\dfrac{38}{3}\right)\sqrt{7}\right)\right)-\left(-2+\dfrac{13}{4}\right)-2\right)\\
&=&\left(\left(-\dfrac{29}{3}\right)\sqrt{7}-\dfrac{109}{8}\right)-\left(\left(\dfrac{3491}{60}\right)\sqrt{7}-\dfrac{13}{4}\right)\\
&=&\left(-\dfrac{29}{3}\right)\sqrt{7}-\dfrac{109}{8}+\left(-\dfrac{3491}{60}\right)\sqrt{7}+\dfrac{13}{4}\\
&=&\left(-\dfrac{1357}{20}\right)\sqrt{7}-\dfrac{83}{8}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{29}{6}\right)\sqrt{28}+\left(0\right)\sqrt{28}+\dfrac{57}{8}-5-\left(\left(\dfrac{9}{4}\right)\sqrt{49}\right)\right)\times\left(\left(\left(-\dfrac{47}{4}\right)\sqrt{63}+\left(\dfrac{19}{2}\right)\sqrt{28}\right)-\left(\left(\left(-\dfrac{19}{2}\right)\sqrt{175}\right)-\left(\left(\dfrac{66}{5}\right)\sqrt{63}\right)-\left(\left(-\dfrac{19}{3}\right)\sqrt{28}\right)\right)-\left(\left(\left(-\dfrac{2}{7}\right)\sqrt{49}\right)+\dfrac{13}{4}\right)-2\right)\\
&=&\left(\left(-\dfrac{29}{3}\right)\sqrt{7}+\left(0\right)\sqrt{7}+\dfrac{57}{8}-5-\dfrac{63}{4}\right)\times\left(\left(\left(-\dfrac{141}{4}\right)\sqrt{7}+\left(19\right)\sqrt{7}\right)-\left(\left(\left(-\dfrac{95}{2}\right)\sqrt{7}\right)-\left(\left(\dfrac{198}{5}\right)\sqrt{7}\right)-\left(\left(-\dfrac{38}{3}\right)\sqrt{7}\right)\right)-\left(-2+\dfrac{13}{4}\right)-2\right)\\
&=&\left(\left(-\dfrac{29}{3}\right)\sqrt{7}-\dfrac{109}{8}\right)\left(\left(\dfrac{3491}{60}\right)\sqrt{7}-\dfrac{13}{4}\right)\\
&=&\left(-\dfrac{101239}{180}\right)\sqrt{49}+\left(-\dfrac{121813}{160}\right)\sqrt{7}+\dfrac{1417}{32}\\
&=&-\dfrac{5605619}{1440}+\left(-\dfrac{121813}{160}\right)\sqrt{7}\\
\end{eqnarray*}