`x^2+4y^2-4x+32y+2078`
`=(x^2-4x+4)+(4y^2+32y+64)+2010`
`=(x^2-2.x.2+2^2)+[(2y)^2+2.2y.8+8^2]+2010`
`=(x-2)^2+(2y+8)^2+2010>=2010`
Dấu = xảy ra khi `{(x-2=0),(2y+8=0):}`
`<=> {(x=2),(y=-4):}`
Vậy `min_(x^2+4y^2-4x+32y+2078)=2010<=>(x;y)=(2;-4)`
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`4x^2+3y^2-2xy-10x-14y+30`
`=(x^2-2xy+y^2)+(2x-2y)+(3x^2-12x+12)+(2y^2-12y+18)`
`=(x-y)^2+2(x-y)+1+3(x^2-4x+4)+2(y^2-6y+9)-1`
`=(x-y+1)^2+3(x-2)^2+2(y-3)^2-1>=-1`
Dấu = xảy ra khi `{(x-y=-1),(x-2=0),(y-3=0):}`
`<=> {(x=2),(y=3):}`
Vậy `min_(4x^2+3y^2-2xy-10x-14y+30)=-1<=>(x;y)=(2;3)`
