L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Soit \( X=\left(\left(\dfrac{65}{8}\right)\sqrt{175}\right)-\left(\left(\dfrac{23}{2}\right)\sqrt{28}\right)-\left(\left(\dfrac{5}{8}\right)\sqrt{175}\right)+\left(-\dfrac{22}{3}\right)\sqrt{175}+\left(-1\right)\sqrt{63}\) et \( Y=\left(\left(-2\right)\sqrt{49}\right)-\left(\left(\left(\dfrac{47}{8}\right)\sqrt{49}\right)-\left(\left(-\dfrac{29}{7}\right)\sqrt{49}\right)-\left(\left(5\right)\sqrt{63}\right)\right)-\left(\left(\left(-\dfrac{15}{4}\right)\sqrt{49}\right)-\dfrac{22}{5}-\left(\left(-\dfrac{13}{2}\right)\sqrt{28}\right)\right)\) . 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(\dfrac{65}{8}\right)\sqrt{175}\right)-\left(\left(\dfrac{23}{2}\right)\sqrt{28}\right)-\left(\left(\dfrac{5}{8}\right)\sqrt{175}\right)+\left(-\dfrac{22}{3}\right)\sqrt{175}+\left(-1\right)\sqrt{63}\right)+\left(\left(\left(-2\right)\sqrt{49}\right)-\left(\left(\left(\dfrac{47}{8}\right)\sqrt{49}\right)-\left(\left(-\dfrac{29}{7}\right)\sqrt{49}\right)-\left(\left(5\right)\sqrt{63}\right)\right)-\left(\left(\left(-\dfrac{15}{4}\right)\sqrt{49}\right)-\dfrac{22}{5}-\left(\left(-\dfrac{13}{2}\right)\sqrt{28}\right)\right)\right)\\
&=&\left(\left(\left(\dfrac{325}{8}\right)\sqrt{7}\right)-\left(\left(23\right)\sqrt{7}\right)-\left(\left(\dfrac{25}{8}\right)\sqrt{7}\right)+\left(-\dfrac{110}{3}\right)\sqrt{7}+\left(-3\right)\sqrt{7}\right)+\left(-14-\left(\dfrac{329}{8}+29-\left(\left(15\right)\sqrt{7}\right)\right)-\left(-\dfrac{105}{4}-\dfrac{22}{5}-\left(\left(-13\right)\sqrt{7}\right)\right)\right)\\
&=&\left(\left(\dfrac{325}{8}\right)\sqrt{7}\right)-\left(\left(23\right)\sqrt{7}\right)-\left(\left(\dfrac{25}{8}\right)\sqrt{7}\right)+\left(-\dfrac{110}{3}\right)\sqrt{7}+\left(-3\right)\sqrt{7}-14-\left(\dfrac{329}{8}+29-\left(\left(15\right)\sqrt{7}\right)\right)-\left(-\dfrac{105}{4}-\dfrac{22}{5}-\left(\left(-13\right)\sqrt{7}\right)\right)\\
&=&\left(-\dfrac{139}{6}\right)\sqrt{7}-\dfrac{2139}{40}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\left(\dfrac{65}{8}\right)\sqrt{175}\right)-\left(\left(\dfrac{23}{2}\right)\sqrt{28}\right)-\left(\left(\dfrac{5}{8}\right)\sqrt{175}\right)+\left(-\dfrac{22}{3}\right)\sqrt{175}+\left(-1\right)\sqrt{63}\right)-\left(\left(\left(-2\right)\sqrt{49}\right)-\left(\left(\left(\dfrac{47}{8}\right)\sqrt{49}\right)-\left(\left(-\dfrac{29}{7}\right)\sqrt{49}\right)-\left(\left(5\right)\sqrt{63}\right)\right)-\left(\left(\left(-\dfrac{15}{4}\right)\sqrt{49}\right)-\dfrac{22}{5}-\left(\left(-\dfrac{13}{2}\right)\sqrt{28}\right)\right)\right)\\
&=&\left(\left(\left(\dfrac{325}{8}\right)\sqrt{7}\right)-\left(\left(23\right)\sqrt{7}\right)-\left(\left(\dfrac{25}{8}\right)\sqrt{7}\right)+\left(-\dfrac{110}{3}\right)\sqrt{7}+\left(-3\right)\sqrt{7}\right)-\left(-14-\left(\dfrac{329}{8}+29-\left(\left(15\right)\sqrt{7}\right)\right)-\left(-\dfrac{105}{4}-\dfrac{22}{5}-\left(\left(-13\right)\sqrt{7}\right)\right)\right)\\
&=&\left(\left(-\dfrac{151}{6}\right)\sqrt{7}\right)-\left(-\dfrac{2139}{40}+\left(2\right)\sqrt{7}\right)\\
&=&\left(-\dfrac{151}{6}\right)\sqrt{7}+\dfrac{2139}{40}+\left(-2\right)\sqrt{7}\\
&=&\left(-\dfrac{163}{6}\right)\sqrt{7}+\dfrac{2139}{40}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\left(\dfrac{65}{8}\right)\sqrt{175}\right)-\left(\left(\dfrac{23}{2}\right)\sqrt{28}\right)-\left(\left(\dfrac{5}{8}\right)\sqrt{175}\right)+\left(-\dfrac{22}{3}\right)\sqrt{175}+\left(-1\right)\sqrt{63}\right)\times\left(\left(\left(-2\right)\sqrt{49}\right)-\left(\left(\left(\dfrac{47}{8}\right)\sqrt{49}\right)-\left(\left(-\dfrac{29}{7}\right)\sqrt{49}\right)-\left(\left(5\right)\sqrt{63}\right)\right)-\left(\left(\left(-\dfrac{15}{4}\right)\sqrt{49}\right)-\dfrac{22}{5}-\left(\left(-\dfrac{13}{2}\right)\sqrt{28}\right)\right)\right)\\
&=&\left(\left(\left(\dfrac{325}{8}\right)\sqrt{7}\right)-\left(\left(23\right)\sqrt{7}\right)-\left(\left(\dfrac{25}{8}\right)\sqrt{7}\right)+\left(-\dfrac{110}{3}\right)\sqrt{7}+\left(-3\right)\sqrt{7}\right)\times\left(-14-\left(\dfrac{329}{8}+29-\left(\left(15\right)\sqrt{7}\right)\right)-\left(-\dfrac{105}{4}-\dfrac{22}{5}-\left(\left(-13\right)\sqrt{7}\right)\right)\right)\\
&=&\left(\left(-\dfrac{151}{6}\right)\sqrt{7}\right)\left(-\dfrac{2139}{40}+\left(2\right)\sqrt{7}\right)\\
&=&\left(\dfrac{107663}{80}\right)\sqrt{7}+\left(-\dfrac{151}{3}\right)\sqrt{49}\\
&=&\left(\dfrac{107663}{80}\right)\sqrt{7}-\dfrac{1057}{3}\\
\end{eqnarray*}