L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(-\dfrac{61}{2}\right)\sqrt{25}\) et \( Y=-\dfrac{74}{9}-\left(\left(-\dfrac{13}{7}\right)\sqrt{45}\right)-\left(\left(0\right)\sqrt{20}\right)-\left(\left(\dfrac{33}{8}\right)\sqrt{25}\right)+\left(\dfrac{52}{3}\right)\sqrt{125}-\dfrac{20}{3}+\left(\left(-\dfrac{31}{3}\right)\sqrt{20}\right)-\left(\left(\dfrac{57}{4}\right)\sqrt{45}\right)-\left(\left(0\right)\sqrt{125}\right)\) . Calculer et simplifier \( X+Y\) , \( X-Y\) et \( X\times Y\) .
Cliquer ici pour afficher la solution
Exercice
\begin{eqnarray*}
X+Y
&=&\left(\left(-\dfrac{61}{2}\right)\sqrt{25}\right)+\left(-\dfrac{74}{9}-\left(\left(-\dfrac{13}{7}\right)\sqrt{45}\right)-\left(\left(0\right)\sqrt{20}\right)-\left(\left(\dfrac{33}{8}\right)\sqrt{25}\right)+\left(\dfrac{52}{3}\right)\sqrt{125}-\dfrac{20}{3}+\left(\left(-\dfrac{31}{3}\right)\sqrt{20}\right)-\left(\left(\dfrac{57}{4}\right)\sqrt{45}\right)-\left(\left(0\right)\sqrt{125}\right)\right)\\
&=&\left(-\dfrac{305}{2}\right)+\left(-\dfrac{74}{9}-\left(\left(-\dfrac{39}{7}\right)\sqrt{5}\right)-\left(\left(0\right)\sqrt{5}\right)-\dfrac{165}{8}+\left(\dfrac{260}{3}\right)\sqrt{5}-\dfrac{20}{3}+\left(\left(-\dfrac{62}{3}\right)\sqrt{5}\right)-\left(\left(\dfrac{171}{4}\right)\sqrt{5}\right)-\left(\left(0\right)\sqrt{5}\right)\right)\\
&=&-\dfrac{305}{2}-\dfrac{74}{9}-\left(\left(-\dfrac{39}{7}\right)\sqrt{5}\right)-\left(\left(0\right)\sqrt{5}\right)-\dfrac{165}{8}+\left(\dfrac{260}{3}\right)\sqrt{5}-\dfrac{20}{3}+\left(\left(-\dfrac{62}{3}\right)\sqrt{5}\right)-\left(\left(\dfrac{171}{4}\right)\sqrt{5}\right)-\left(\left(0\right)\sqrt{5}\right)\\
&=&-\dfrac{13537}{72}+\left(\dfrac{807}{28}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(-\dfrac{61}{2}\right)\sqrt{25}\right)-\left(-\dfrac{74}{9}-\left(\left(-\dfrac{13}{7}\right)\sqrt{45}\right)-\left(\left(0\right)\sqrt{20}\right)-\left(\left(\dfrac{33}{8}\right)\sqrt{25}\right)+\left(\dfrac{52}{3}\right)\sqrt{125}-\dfrac{20}{3}+\left(\left(-\dfrac{31}{3}\right)\sqrt{20}\right)-\left(\left(\dfrac{57}{4}\right)\sqrt{45}\right)-\left(\left(0\right)\sqrt{125}\right)\right)\\
&=&\left(-\dfrac{305}{2}\right)-\left(-\dfrac{74}{9}-\left(\left(-\dfrac{39}{7}\right)\sqrt{5}\right)-\left(\left(0\right)\sqrt{5}\right)-\dfrac{165}{8}+\left(\dfrac{260}{3}\right)\sqrt{5}-\dfrac{20}{3}+\left(\left(-\dfrac{62}{3}\right)\sqrt{5}\right)-\left(\left(\dfrac{171}{4}\right)\sqrt{5}\right)-\left(\left(0\right)\sqrt{5}\right)\right)\\
&=&\left(-\dfrac{305}{2}\right)-\left(-\dfrac{2557}{72}+\left(\dfrac{807}{28}\right)\sqrt{5}\right)\\
&=&-\dfrac{305}{2}+\dfrac{2557}{72}+\left(-\dfrac{807}{28}\right)\sqrt{5}\\
&=&-\dfrac{8423}{72}+\left(-\dfrac{807}{28}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(-\dfrac{61}{2}\right)\sqrt{25}\right)\times\left(-\dfrac{74}{9}-\left(\left(-\dfrac{13}{7}\right)\sqrt{45}\right)-\left(\left(0\right)\sqrt{20}\right)-\left(\left(\dfrac{33}{8}\right)\sqrt{25}\right)+\left(\dfrac{52}{3}\right)\sqrt{125}-\dfrac{20}{3}+\left(\left(-\dfrac{31}{3}\right)\sqrt{20}\right)-\left(\left(\dfrac{57}{4}\right)\sqrt{45}\right)-\left(\left(0\right)\sqrt{125}\right)\right)\\
&=&\left(-\dfrac{305}{2}\right)\times\left(-\dfrac{74}{9}-\left(\left(-\dfrac{39}{7}\right)\sqrt{5}\right)-\left(\left(0\right)\sqrt{5}\right)-\dfrac{165}{8}+\left(\dfrac{260}{3}\right)\sqrt{5}-\dfrac{20}{3}+\left(\left(-\dfrac{62}{3}\right)\sqrt{5}\right)-\left(\left(\dfrac{171}{4}\right)\sqrt{5}\right)-\left(\left(0\right)\sqrt{5}\right)\right)\\
&=&\left(-\dfrac{305}{2}\right)\left(-\dfrac{2557}{72}+\left(\dfrac{807}{28}\right)\sqrt{5}\right)\\
&=&\dfrac{779885}{144}+\left(-\dfrac{246135}{56}\right)\sqrt{5}\\
&=&\dfrac{779885}{144}+\left(-\dfrac{246135}{56}\right)\sqrt{5}\\
\end{eqnarray*}