解方程组 x²+2xy+y²=25 （x-y）²-3x+3y+2=0

x²+2xy+y²=25 (1)
(x-y)²-3x+3y+2=0 (2)
由(1)得(x+y)²=25
x+y=5或x+y=-5
由(2)得
(x-y)²-3(x-y)+2=0
(x-y-1)(x-y-2)=0
x-y=1或x-y=2
分4种情况讨论：
x+y=5 x-y=1时，解得x=3 y=2
x+y=-5 x-y=1时，解得x=-2 y=-3
x+y=5 x-y=2时，解得x=7/2 y=3/2
x+y=-5 x-y=2时，解得x=-3/2 y=-7/2
综上，得共有4组
x=3 y=2或x=-2 y=-3或x=7/2 y=3/2或x=-3/2 y=-7/2

(x+y)^2=25, 则有x+y=正负5
(x-y)^2-3(x-y)+2=0, (x-y-2)(x-y-1)=0, so x-y=2 or x-y=1
有四种可能
x+y=5 x-y=2 x=7/2 y=3/2
x+y=5 x-y=1 x=3 y=2
x+y=-5 x-y=2 x=-3/2 y=-7/2
x+y=-5 x-y=1 x=-2 y=-3

(x+y)²=25,(x-y)²-3(x-y)+2=0
所以x+y=5或-5 (x-y-1)*(x-y-2)=0
x+y=5或-5,x-y=1或2
解得x=3,y=2或x=7/2,y=3/2或x=-2,y=-3或x=-3/2,y=-7/2.