已知实数ab满足4a²+b²=4ab,则b/a+a/b=

已知实数ab满足4a²+b²=4ab,则b/a+a/b=
已知实数ab满足4a²+b²=4ab,则b/a+a/b=

已知实数ab满足4a²+b²=4ab,则b/a+a/b=
4a²+b²=4ab,
4a^2-4ab+b^2=0
(2a-b)^2=0
2a-b=0
2a=b
b/a=2a/a=2
a/b=a/(2a)=1/2
b/a+a/b==2+1/2=5/2

4a²+b²=4ab
4a²+b²-4ab=0
(2a-b)²=0
2a-b=0
b=2a
b/a+a/b
=2a/a+a/2a
=2+1/2
=5/2

4a²+b²=4ab，移项，（2a-b）^2=0,所以2a=b.
所以
b/a+a/b=5/2