解方程组{x²＋2xy+y²=25,﹙x－y﹚²－3x+3y+2=0}

x²＋2xy+y²=25,即(x+y)²=25得x+y=±5
﹙x－y﹚²－3x+3y+2=0
(x-y)²-3(x-y)+2=0
(x-y-1)(x-y-2)=0
得x-y=1或x-y=2
所以原方程组可化为
x+y=5,x-y=1 解得x=3,y=2
x+y=5,x-y=2 解得x=3.5,y=1.5
x+y=-5,x-y=1 解得x=-2,y=-3
x+y=-5,x-y=2 解得x=-1.5,y=-3.5