$H =\dfrac{x^2}{x-2} $
$=\dfrac{x^2-4+4}{x-2} $
$=x+2+\dfrac{4}{x-2} $
$=x-2+\dfrac{4}{x-2} + 4 ≥ 2\sqrt[]{4} + 4 = 2.2+4= 8$
Dấu =" xảy ra $⇔x-2=2⇔x=4$
$K = \dfrac{x^2}{x-3} $
$=x+3 +\dfrac{9}{x-3} $
$=x-3+\dfrac{9}{x-3} + 6 ≥2\sqrt[]{9} + 6 = 2.3+6=12$
Dấu "=" xảy ra $⇔x-3=3 ⇔x=6$
$L = \dfrac{x^2-x+5}{x-2} $
$=\dfrac{(x-2)^2+3.(x-2) +7}{x-2} $
$=x-2+ \dfrac{7}{x-2} + 3 ≥ 2\sqrt[]{7}+3 = 3+2\sqrt[]{7}$
Dấu "=" xay ra $⇔x=2+\sqrt[]{7}$
