Đáp án:
`3x^2 + y^2 + z^2 + 2x - 2y + 2xy + 3 = 0`
`<=>(x^2 + y^2 + 1 + 2xy - 2y - 2x) + ( 2x^2 + 4x + 2) + z^2 = 0`
`<=> (x^2 + y^2 + 1 + 2xy - 2y - 2x) + 2(x^2 + 2x + 1) + z^2 =0`
`<=> (x+y-1)^2 + 2(x+1)^2 + z^2=0`
Có `{((x+y-1)²≥0),((x+1)²≥0),(z^2 ≥0):} AA x, y, z in RR`
`=> (x+y-1)^2 + 2(x+1)^2 + z^2≥0`
Dấu '`=`' xảy ra`<=> {((x+y-1)²=0),((x+1)²=0),(z^2 =0):}`
`<=>` `{(x=-1),(y=2),(z=0):}`