`#tnvt`
`-x^2-y^2+2x-6y+9`
`=-x^2+2x-1-y^2-6y-9+19`
`=-(x^2-2x+1)-(y^2+6y+9)+19`
`=-(x-1)^2-(y+3)^2+19`
`=-[(x-1)^2+(y+3)^2]+19`
`∀x,y` ta có: `{((x-1)^2>=0),((y+3)^2>=0):}`
`=>(x-1)^2+(y+3)^2>=0`
`=>-[(x-1)^2+(y+3)^2]<=0`
`=>-[(x-1)^2+(y+3)^2]+19<=19`
Dấu `=` xảy ra khi `{((x-1)^2=0),((y+3)^2=0):}`
`<=>{(x-1=0),(y+3=0):}`
`<=>{(x=1),(y=-3):}`
Vậy `GTLNN=19` khi `(x;y)=(1;-3)`
