ĐKXĐ : `x > 2`
`P = 5`
`⇔ (x+sqrt{x-2}+2)/(sqrt{x-2}) = 5`
`⇔ x +sqrt{x-2}+2=5sqrt{x-2}`
`⇔ x + sqrt{x-2} + 2 - 5sqrt{x-2} = 0`
`⇔ -4sqrt{x-2} + x - 2 = 0`
`⇔ -4sqrt{x-2} = -x - 2`
`⇔ (-4sqrt{x-2})^2 = (-x-2)^2`
`⇔ 16(x-2) = x^2 + 4x + 4`
`⇔ 16x - 32 = x^2 + 4x + 4`
`⇔ 16x - 32 - x^2 + 4x - 4 = 0`
`⇔ -x^2 + 12x - 36 = 0`
`\Delta = 12^2 -4(-1)(-36) = 0`
Vậy pt có nghiệm kẹp :
`x_1 = x_2 = (-12)/(2(-1)) = 6(TM)`
Vậy `S = {6}`
