已知4x^2+4x+3=y^2+4y.求x-y的值

已知4x^2+4x+3=y^2+4y.求x-y的值
已知4x^2+4x+3=y^2+4y.求x-y的值

已知4x^2+4x+3=y^2+4y.求x-y的值
题目有问题,3前面应该是-号吧,不然没法做.
4x²+4x-3=y²+4y
4x²+4x+1-y²-4y-4=0
(2x+1)²-(y+2)²=0
平方项恒非负,两平方项之和=0,两平方项都=0
2x+1=0 x=-1/2
y+2=0 y=-2
x-y=-(1/2)-(-2)=3/2
如果题目是这样的,那么题目肯定错了,3前面应该是-号.

条件不足

令m = x - y ∴ y = x-m
4x^2 + 4x +3 = x^2-2mx + m^2 + 4x - 4m
3x^2 +2mx +3-m^2+4m = 0
△ = 4m^2 -12(3-m^2+4m) = 0
9-3m^2+12m = m^2
4m^2 - 12m -9 = 0
m=(3±3√2)/2