`x^2 + 2y^2 + 2xy + 6x + 9y + 10`
`= (x^2 + 2xy + 6x) + 2y^2 + 9y + 10`
`= [x^2 + 2x(y + 3) + (y + 3)^2] - (y + 3)^2 + 2y^2 + 9y + 10`
`= (x + y + 3)^2 - y^2 - 6y - 9 + 2y^2 + 9y + 10`
`= (x + y + 3)^2 + y^2 + 3y + 1`
`= (x + y + 3)^2 + y^2 + 3y + 9/4 - 5/4`
`= (x + y + 3)^2 + (y + 3/2)^2 - 5/4 ≥ -5/4`
Dấu `=` xảy ra `⇔`$\left \{ {{y+3/2=0} \atop {x+y+3=0}} \right.$
`⇔` $\left \{ {{y=-3/2} \atop {x=-9/2}} \right.$
Vậy GTNN là `-5/4 ⇔ x = -9/2` và `y = -3/2`
