a+b+c=1,求证(1+1/a)(1+1/b)(1+1/c)>=64

日期：2022-03-29 01:38:28 人气：1

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) +
    A+
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