Tìm GTNN `C=x^2-4xy+5y^2+10x-22y+28`

`C = x^2 - 4xy + 5y^2 + 10x - 22y + 28`

`= x^2 - 4xy + 4y^2 + 10x - 20y - 2y + y^2 + 1 + 27`

`= (x -2y)^2 + 10(x - 2y) + (y -1)^2 + 27`

`= [(x -2y)^2 + 2 * 5(x - 2y) + 25] + (y - 1)^2 + 2`

`= (x - 2y + 5)^2 + (y -1)^2 + 2`

Ta có `:`

` (x - 2y + 5)^2  >= 0 AA x`

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

`=> (x - 2y + 5)^2 + (y -1)^2 + 2 >= 2 AA x`

Dấu ''`=`'' xảy ra `<=> {(x - 2y +5 = 0),(y -1 = 0):} <=> x = -3; y = 1`

Vậy GTNN của `C = 2 <=> x = -3; y = 1`