Theo hệ thức Viet: \(\left\{{}\begin{matrix}x_1+x_2=19\\x_1x_2=9\end{matrix}\right.\)
Ta có: \(\left(\sqrt{x_1}+\sqrt{x_2}\right)^2=x_1+x_2+2\sqrt{x_1x_2}=19+2\sqrt{9}=25\)
\(\Rightarrow\sqrt{x_1}+\sqrt{x_2}=5\) (do \(\sqrt{x_1}+\sqrt{x_2}>0\))
Do đó:
\(T=\dfrac{\left(\sqrt{x_1}\right)^3+\left(\sqrt{x_2}\right)^3}{\left(x_1+x_2\right)^2-2x_1x_2}=\dfrac{\left(\sqrt{x_1}+\sqrt{x_2}\right)\left(x_1+x_2-\sqrt{x_1x_2}\right)}{\left(x_1+x_2\right)^2-2x_1x_2}\)
\(=\dfrac{5.\left(19-\sqrt{9}\right)}{19^2-2.9}=\dfrac{80}{343}\)
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