L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Soit \( X=\left(\dfrac{49}{5}\right)\sqrt{25}\) et \( Y=\left(\left(\left(-\dfrac{8}{3}\right)\sqrt{125}\right)-\left(\left(-\dfrac{1}{4}\right)\sqrt{125}\right)+\dfrac{7}{2}\right)-\left(\left(4\right)\sqrt{45}\right)-\left(-\dfrac{22}{7}+\dfrac{17}{4}\right)\) . 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{49}{5}\right)\sqrt{25}\right)+\left(\left(\left(\left(-\dfrac{8}{3}\right)\sqrt{125}\right)-\left(\left(-\dfrac{1}{4}\right)\sqrt{125}\right)+\dfrac{7}{2}\right)-\left(\left(4\right)\sqrt{45}\right)-\left(-\dfrac{22}{7}+\dfrac{17}{4}\right)\right)\\
&=&\left(49\right)+\left(\left(\left(\left(-\dfrac{40}{3}\right)\sqrt{5}\right)-\left(\left(-\dfrac{5}{4}\right)\sqrt{5}\right)+\dfrac{7}{2}\right)-\left(\left(12\right)\sqrt{5}\right)-\left(-\dfrac{22}{7}+\dfrac{17}{4}\right)\right)\\
&=&49+\left(\left(\left(-\dfrac{40}{3}\right)\sqrt{5}\right)-\left(\left(-\dfrac{5}{4}\right)\sqrt{5}\right)+\dfrac{7}{2}\right)-\left(\left(12\right)\sqrt{5}\right)-\left(-\dfrac{22}{7}+\dfrac{17}{4}\right)\\
&=&\dfrac{1439}{28}+\left(-\dfrac{289}{12}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X-Y
&=&\left(\left(\dfrac{49}{5}\right)\sqrt{25}\right)-\left(\left(\left(\left(-\dfrac{8}{3}\right)\sqrt{125}\right)-\left(\left(-\dfrac{1}{4}\right)\sqrt{125}\right)+\dfrac{7}{2}\right)-\left(\left(4\right)\sqrt{45}\right)-\left(-\dfrac{22}{7}+\dfrac{17}{4}\right)\right)\\
&=&\left(49\right)-\left(\left(\left(\left(-\dfrac{40}{3}\right)\sqrt{5}\right)-\left(\left(-\dfrac{5}{4}\right)\sqrt{5}\right)+\dfrac{7}{2}\right)-\left(\left(12\right)\sqrt{5}\right)-\left(-\dfrac{22}{7}+\dfrac{17}{4}\right)\right)\\
&=&\left(49\right)-\left(\left(-\dfrac{289}{12}\right)\sqrt{5}+\dfrac{67}{28}\right)\\
&=&49+\left(\dfrac{289}{12}\right)\sqrt{5}-\dfrac{67}{28}\\
&=&\dfrac{1305}{28}+\left(\dfrac{289}{12}\right)\sqrt{5}\\
\end{eqnarray*}
\begin{eqnarray*}
X\times Y
&=&\left(\left(\dfrac{49}{5}\right)\sqrt{25}\right)\times\left(\left(\left(\left(-\dfrac{8}{3}\right)\sqrt{125}\right)-\left(\left(-\dfrac{1}{4}\right)\sqrt{125}\right)+\dfrac{7}{2}\right)-\left(\left(4\right)\sqrt{45}\right)-\left(-\dfrac{22}{7}+\dfrac{17}{4}\right)\right)\\
&=&\left(49\right)\times\left(\left(\left(\left(-\dfrac{40}{3}\right)\sqrt{5}\right)-\left(\left(-\dfrac{5}{4}\right)\sqrt{5}\right)+\dfrac{7}{2}\right)-\left(\left(12\right)\sqrt{5}\right)-\left(-\dfrac{22}{7}+\dfrac{17}{4}\right)\right)\\
&=&\left(49\right)\left(\left(-\dfrac{289}{12}\right)\sqrt{5}+\dfrac{67}{28}\right)\\
&=&\left(-\dfrac{14161}{12}\right)\sqrt{5}+\dfrac{469}{4}\\
&=&\left(-\dfrac{14161}{12}\right)\sqrt{5}+\dfrac{469}{4}\\
\end{eqnarray*}