$$\eqalign{
& (3{x^2} + 11)\sqrt {{x^2} + 1} = 3\sqrt 3 {x^3} - 8{x^2} + 11\sqrt 3 x + 4 \cr
& \Leftrightarrow (3{x^2} + 11)\sqrt {{x^2} + 1} = (3{x^2} + 11)\sqrt 3 x - 8{x^2} + 4 \cr
& \Leftrightarrow (3{x^2} + 11)(\sqrt {{x^2} + 1} - \sqrt 3 x) = - 8{x^2} + 4 \cr
& \Leftrightarrow (3{x^2} + 11)(\frac{{1 - 2{x^2}}}{{\sqrt {{x^2} + 1} + \sqrt 3 x}}) = 4(1 - 2{x^2}) \cr
& \Leftrightarrow (3{x^2} + 11)(1 - 2{x^2})(\frac{1}{{\sqrt {{x^2} + 1} + \sqrt 3 x}} - 4) = 0 \cr} $$
tới đây tui hết biết rồi.