`C=2x^2+3y^2+4xy-8x-2y+18`
`C=2x^2+2y^2+y^2+4xy-8x-8y+6y+9+9`
`C=(2x^2+4xy+2y^2)+(y^2+6y+9)+(-8x-8y)+9`
`C=2(x^2+2xy+y^2)+(y+3)^2-8(x+y)+9`
`C=2(x+y)^2+(y+3)^2-8(x+y)+9`
`C=2(x+y)^2+(y+3)^2-8(x+y)+8+1`
`C=[2(x+y)^2-8(x+y)+8]+(y+3)^2+1`
`C=2[(x+y)^2-4(x+y)+4]+(y+3)^2+1`
`C=2(x+y-2)^2+(y+3)^2+1`
Ta có:
`2(x+y-2)^2≥0 ∀x,y`
`(y+3)^3≥0∀y`
`⇒2(x+y-2)+(y+3)^3+1≥1∀x,y`
Vậy Min`C` bằng `1` khi `y=-3;x=5`
