已知a,b,c均为正数且a+b+c=1求证(1+1/a)(1+1/b)(1+1/c)≥64

(1+1/a)(1+1/b)(1+1/c)
=1+ (1/a+1/b+1/c) + (1/ab+1/bc+1/ca) +1/abc
=1+ (1/a+1/b+1/c) + (a+b+c)/abc +1/abc
=1+ (1/a+1/b+1/c) + 2/abc
其中由柯西不等式，
(1/a+1&#