Question

若实数a b满足b/a+a/b=2则a²+ab+b²/a²+4ab+b²的值为?

Answer 1

b/a+a/b=2
a²+b²=2ab
a²+ab+b²/a²+4ab+b²
=2ab+ab/2ab+4ab
=3ab/6ab
=1/2

Answer 2

即(a²+b²)/ab=2
a²+b²=2ab
所以原式=(2ab+ab)/(2ab+4ab)
=3ab/6ab
=1/2