Có `x^2-2xy+6y^2-12x+2y+41=0`
`<=>x^2-2x(y+6)+(y+6)^2-y^2-12y-36+6y^2+2y+41=0`
`<=>(x-y-6)^2+5y^2-10y+5=0`
`<=>(x-y-6)^2+5(y^2-2y+1)=0`
`<=>(x-y-6)^2+5(y-1)^2=0`
Mà
`(x-y-6)^2≥0`
`(y-1)^2≥0`
Do đó `x-y-6=y-1=0`
`<=>x-y=6;y=1`
`<=>x=7;y=1`
Thay vào A ta có
`A= (2020-2019(9-7-1)^2019-(7-6)^2018)/(1.1010)`
`=(2020-2019-1)/1`1010`
`=0`