(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)=a^2+196*4/(a^2)
>=2√[(a^2)*(196*4/(a^2))]
=56 當(dāng)且僅當(dāng)a=2√7,b=√7時(shí)等號(hào)成立
故a=2√7,b=√7時(shí)最小值為56