Đáp án:
`S={(-3+\sqrt3)/3;(3-\sqrt3)/3;\sqrt6\;-\sqrt6}`
Giải thích các bước giải:
` (x^2)/(x+2)^2=3x^2-6x-3`
`<=>x^2=(x+2)^2(3x^2-6x-3)`
`<=>x^2=(x^2+4x+4)(3x^2-6x-3)`
`<=>x^2=3x^4-6x^3-3x^2+12x^3-24x^2-12x+12x^2-24x-12`
`<=>3x^4+6x^3-16x^2-36x-12=0`
`<=>3x^4+6x^3+2x^2-18x^2-36x-12=0`
`<=>x^2(3x^2+6x+2)-6(3x^2+6x+2)=0`
`<=>(3x^2+6x+2)(x^2-6)=0`
`<=>`\(\left[ \begin{array}{l}3x^2+6x+2=0(1)\\x^2-6=0(2)\end{array} \right.\)
Gỉai `(1): 3x^2+6x+2=0`
`<=>x=(-3+\sqrt3)/3;x=(3-\sqrt3)/3`
`(2)x^2-6=0`
`<=>x^2=6`
`<=>x=+-\sqrt6`
Vậy `S={(-3+\sqrt3)/3;(3-\sqrt3)/3;\sqrt6\;-\sqrt6}`
