[TEX]A = \frac{x^4 + 1}{x(x-1)(x+1)} = \frac{x^4 + 1}{x^3 - x} [/TEX]
[TEX]= \frac{x^2 + \frac{1}{x^2}}{x - \frac{1}{x}}[/TEX]
đặt [TEX]x - \frac{1}{x} = t \Rightarrow t^2 = x^2 + \frac{1}{x^2} -2 [/TEX]
[TEX]\Rightarrow x^2 + \frac{1}{x^2} = t^2 + 2[/TEX]
[TEX]\Rightarrow A = \frac{t^2 + 2}{t} = t + \frac{2}{t} \geq 2\sqrt{2}[/TEX]
[TEX]" = " \Leftrightarrow x = \frac{\sqrt{2} + \sqrt{6}}{2}[/TEX]