已知a>b>0求(a^3b-a^2b^2+196)/(ab-b^2)的最小值

(a^3b-a^2b^2+196)/(ab-b^2)
=（a^3b-a^2b^2)/(ab-b^2)+196/(ab-b^2)
=a^2+196/(b(a-b))
b(a-b)<=[(b+a-b)/2]^2=(a^2)/4当且仅当a=2b等号成立
所以a^2+196/(b(a-b))>=a^2+196*4/(a^2)
>=2√[(a^2)*(196*4/(a^2))]
=56 当且仅当a=2√7,b=√7时等号成立
故a=2√7,b=√7时最小值为56