tìm max `2x^2+4y^2-4xy-4x-4y+2023`

`color{pink}{@haanh}`

`C=2x^2+4y^2-4xy-4x-4y+2023`

`=2(x^2-2x-2xy)+4y^2-4y+2023`

`=2(x^2-2x(y+1)+(y+1)^2]-2(y+1)^2+4y^2-4y+2023`

`=2(x-y-1)^2-2(y^2+2y+1)+4y^2-4y+2023`

`=2(x-y-1)^2-2y^2-4y-2+4y^2-4y+2023`

`=2(x-y-1)^2+2y^2-8y+2021`

`=2(x-y-1)^2+2(y^2-4y+4)+2013`

`=2(x-y-1)^2+2(y-2)^2+2013ge2013`

Dấu `"="` xảy ra khi và chỉ khi `:` $\left \{ {{y-2=0} \atop {x-y-1=0}} \right.$ 

`<=>` $\left \{ {{y=2} \atop {x=3}} \right.$

Vậy `Min_C=2013` Tại `x=3;y=2`