求满足条件5X的平方+5Y的平方+8XY+2Y-2X+2=0的实数 X,Y

由5x^2 + 5y^2 + 8xy +2y -2x +2 = 0
(4x^2 + 4y^2 + 8xy) + (x^2-2x+1) + (y^2+2y+1) = 0
4(x+y)^2 + (x-1)^2 + (y+1)^2 = 0
因完全平方式不小于0
则有
x+y = 0
x-1 = 0
y+1 = 0
解得
x= 1,y = -1