`A=2x^2 +y^2 -2xy-2x+3`

  `=x^2 -2xy+y^2 +x^2 -2x+1+2`

  `=(x-y)^2 +(x-1)^2 +2`

Vì `(x-y)^2 >= 0 AA x,y `

    `(x-1)^2 >= 0 AA x`

`=>(x-y)^2 + (x-1)^2 >= 0 AA x,y`

`=>(x-y)^2 + (x-1)^2 +2 >= 2 AA x,y`

`-> A >= 2`

Dấu "=" xảy ra khi : `{(x-y=0),(x-1=0):}`
                             `<=>{(x=y),(x=1):}`

                             `<=>x=y=1`

Vậy `A_(min) =2` khi `x=y=1`