解方程组:x^2-2xy-y^2+2x+y+2=0,2x^2-4xy-2y^2+3x+3y+4=0

问题描述:

解方程组:x^2-2xy-y^2+2x+y+2=0,2x^2-4xy-2y^2+3x+3y+4=0

x^2-2xy-y^2=-2x-y-2=-(3x+3y+4)/2
4x+2y+4=3x+3y+4
x=y

我用计算机算的
答案是{{x -> -(1/2), y -> -(1/2)}, {x -> 2, y -> 2}}

x^2-2xy-y^2+2x+y+2=0,(1)2x^2-4xy-2y^2+3x+3y+4=0 ,(2)(1)式*2得2x^2-4xy-2y^2+4x+2y+4=0,(3)(2)式-(3)式得-x+y=0x=y代入(1)y^2-2y^2-y^2+2y+y+2=02y^2-3y-2=0(y-2)(2y+1)=0y1=2,y2=-1/2x1=2,x2=-1/2解是;x1=y1=-1/...