~ Gửi bạn nhea ~
ĐKXĐ: `x \ge 0`
`sqrt{x^2+2x} + sqrt{x^2-x} = 2|x|`
`⇔ (sqrt{x^2+2x}+sqrt{x^2-x})^2 = (2|x|)^2`
`⇔ x^2 + 2x + 2sqrt{(x^2+2x)(x^2-x)} + x^2 - x = 4|x|^2`
`⇔ 2x^2 + x + 2sqrt{x^4+x^3-2x^2} = 4x^2`
`⇔ 2sqrt{x^4+x^3-2x^2} = 2x^2 - x`
`⇔ (2sqrt{x^4+x^3-2x^2})^2 = (2x^2-x)^2`
`⇔ 4(x^4+x^3-2x^2) = 4x^4 - 4x^3 + x^2`
`⇔ 4x^4 + 4x^3 - 8x^2 - 4x^4 + 4x^3 - x^2 = 0`
`⇔ (4x^4-4x^4) + (4x^3+4x^3) - (8x^2+x^2) = 0`
`⇔ 8x^3 - 9x^2 = 0`
`⇔ x^2(8x-9) = 0`
TH1 : `x^2 = 0 ⇔ |x| = 0 ⇔ x = 0(TM)`
TH2 `8x - 9 = 0 ⇔ 8x = 9 ⇔ x = 9/8(TM)`
Vậy `S = {0,9/8}`
