`#laviken#`
Gọi `A=2x^2+3y^2-2xy+4x-7y+2012`
`A=2x^2+3y^2-2xy+4x-7y+2012`
`2A=2(2x^2+3y^2-2xy+4x-7y+2012)`
`2A=4x^2+6y^2-4xy+8x-14y+4024`
`=(4x^2-4xy+y^2)+5y^2+8x-14y+4024`
`=(2x-y)^2+4(2x-y)+5y^2-10y+4024`
`=(2x-y)^2+4(2x-y)+4+5(y^2-y+1)+4015`
`=(2x-y+2)^2+5(y-1)^2+4015\ge4015`
`=>A\ge4015/2`
Vậy `Amin=4015/2` khi `(x,y)=((-1)/2,1)`