二元二次方程组x2+y2+2xy=9 (x-y)2-3x+3y+2=0
问题描述：
二元二次方程组x2+y2+2xy=9 (x-y)2-3x+3y+2=0
答
x^2+y^2+2xy=9 (1)
(x-y)^2-3x+3y+2=0 (2)
整理得:
(x+y)^2=9
x+y=3
x+y=-3
(x-y)^2-3x+3y+2=0
(x-y)^2-3(x-y)+2=0
[(x-y)-1][(x-y)-2]=0
x-y=1
x-y=2
得到方程组:
x+y=3 (1)
x-y=1 (2)
(1)+(2)得:
2x=4
x=2
解方程组得：
x=2
y=1
得到方程组:
x+y=-3 (1)
x-y=2 (2)
(1)+(2)得:
2x=-1
x=-1/2
解方程组得：
x=-1/2
y=-5/2
答
x2+y2+2xy=9(x+y)²=9x+y=3或-3(x-y)2-3x+3y+2=0(x-y)²-3(x-y)+2=0(x-y-1)(x-y-2)=0x-y=1或2所以组成4个方程组x+y=3,x-y=1x+y=3,x-y=2x+y=-3,x-y=1x+y=-3,x-y=2所以x=2,y=1x=5/2,y=1/2x=-1,y=2x=-1/2,y=-5/...