` (x + 1)\sqrt{x^2 - 2x + 3} = x^2 + 1 `
` <=> (x + 1)^{2}(x^2 - 2x + 3) = x^4 + 2x^2 + 1 `
` <=> (x^2 + 2x + 1)(x^2 - 2x + 3) = x^4 + 2x^2 + 1 `
` <=> x^4 - 2x^3 + 3x^2 + 2x^3 - 4x^2 + 6x + x^2 - 2x + 3 = x^4 + 2x^2 + 1 `
` <=> 3x^2 - 4x^2 + 6x + x^2 - 2x + 3 = 2x^2 + 1 `
` <=> 4x + 3 = 2x^2 + 1 `
` <=> 4x + 3 - 2x^2 - 1 = 0 `
` <=> -2x^2 + 4x + 2 = 0 `
` <=> -2(x^2 - 2x - 1) = 0 `
` <=> x^2 - 2x - 1 = 0 `
` <=> x = \frac{-(-2) ± \sqrt{(-2)^2 - 4.1.(-1)}}{2.1} `
` <=> x = \frac{2 ± \sqrt{8}}{2} `
` <=> x = \frac{2 ± 2\sqrt{2}}{2} `
` <=> x = 1 ± \sqrt{2} `
` <=> ` \(\left[ \begin{array}{l}x_1=1+\sqrt{2}\\x_2=1-\sqrt{2}\end{array} \right.\)
Vậy ` S = {1 + \sqrt{2} ; 1 - \sqrt{2}} `
