(ab+a+b+1)(ab+ac+bc+c^2)>=16abc

题目

(ab+a+b+1)(ab+ac+bc+c^2)>=16abc

答案

(ab+a+b+1)(ab+ac+bc+c^2)
=(a+1)(b+1)(a+c)(b+c)
>=2sqrt(a*1)*2sqrt(b*1)*2sqrt(a*c)*2sqrt(b*c)
=16sqrt(a*b*a*c*b*c)
=16abc
漏条件a,b,c>0