2a+b=ab
(2a+b)/ab=1
2/b + 1/a =1
所以
(a+2b)=(a+2b)*(2/b + 1/a ) 相乘展开
=4+1+2a/b +2b/a
≥5+2*根号(2a/b *2b/a)
=5+2*2=9
当且仅当2a/b =2b/a 即a=b=3 时取等
若a大于0,b大于0,2a+b=ab,则a+2b最小值为多少?
2a+b=ab
(2a+b)/ab=1
2/b + 1/a =1
所以
(a+2b)=(a+2b)*(2/b + 1/a ) 相乘展开
=4+1+2a/b +2b/a
≥5+2*根号(2a/b *2b/a)
=5+2*2=9
当且仅当2a/b =2b/a 即a=b=3 时取等