A) \(^{x^2-4x+1< 0}\)
⇔ x2 - (2- √3)x -(2+√3)x +4-3 <0
⇔ x2-(2-√3)x - (2+√3) x + (2-√3)(2+√3) <0
⇔ x(x-2+√3) - (2+√3)( x-2+√3) <0
⇔ (x- 2-√3)(x-2+√3) < 0
⇔\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x-2+\sqrt{3}< 0\\x-2-\sqrt{3}>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-2+\sqrt{3}>0\\x-2-\sqrt{3}< 0\end{matrix}\right.\end{matrix}\right.\)
⇔\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 2-\sqrt{3}\\x>2+\sqrt{3}\end{matrix}\right.\left(ktm\right)}\\\left\{{}\begin{matrix}x>2-\sqrt{3}\\x< 2+\sqrt{3}\end{matrix}\right.\left(tm\right)}\end{matrix}\right.\)⇔ 2-√3 < x < 2+√3
B) 3x2-x+1>0
⇔ 3x2-2.√3.x.\(\frac{1}{2}\) + \(\frac{1}{4}+\frac{3}{4}\)>0
⇔ (√3.x-\(\frac{1}{2}\))2 + \(\frac{3}{4}\) >0 ∀ x ϵ R
