若a2+b2+a-2b+5/4=0,则a−ba+b=_.

问题描述:

若a2+b2+a-2b+

5
4
=0,则
a−b
a+b
=______.

a2+b2+a-2b+

5
4
=0可化为a2+a+
1
4
+b2-2b+1=0,
即(a+
1
2
2+(b-1)2=0,
于是a=-
1
2
,b=1.
a−b
a+b
=
1
2
−1
1
2
+1
=-3.