6x²+11xy+3y²+4x-y-2

6x²+11xy+3y²+4x-y-2

=(3x+y-1)(2x+3y+2)
十字相乘复杂版
后面的4x-y=2(3x+y)-(2x+3y)

4X^2+Y^2+XY=1化简得(x/2+y)^2+(15/4)x^2=1
令(√15/2)x=rcosθ，x/2+y=rsinθ(其中r=1)->y=sinθ-(1/√15)cosθ带入2X+Y得
θ=arctan(√3/√5)=37.76°,max(2X+Y)=sinθ+(3/√15)cosθ