\(\sqrt{3x^2-9x+1}=x-2\) (ĐK: \(x>2\) )
\(\Leftrightarrow3x^2-9x+1=\left(x-2\right)^2\)
\(\Leftrightarrow3x^2-9x+1=x^2-4x+4\)
\(\Leftrightarrow3x^2-9x+1-x^2+4x-4=0\)
\(\Leftrightarrow2x^2-5x-3=0\)
\(\Rightarrow\Delta=\left(-5\right)^2-4\cdot2\cdot\left(-3\right)=49>0\)
Vậy pt có 2 nghiệm:
\(\left\{{}\begin{matrix}x_1=\dfrac{-\left(-5\right)+\sqrt{49}}{2\cdot2}=3\\x_2=\dfrac{-\left(-5\right)-\sqrt{49}}{2\cdot2}=-\dfrac{1}{2}\left(ktm\right)\end{matrix}\right.\)
Vậy: \(S=\left\{3\right\}\)
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