a>b>0,证2^a+1/2^a>2^b+1/2^b.

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a>b>0,证2^a+1/2^a>2^b+1/2^b.
a>b>0,证2^a+1/2^a>2^b+1/2^b.

a>b>0,证2^a+1/2^a>2^b+1/2^b.
a>b>0,
2^a+1/2^a-2^b-1/2^b=2^a-2^b+1/2^a-1/2^b=[(2^a-2^b)2^a*2^b+(2^b-2^a)]/2^a*2^b=
(2^a-2^b)(2^a*2^b-1)/2^a*2^b
2^a>2^b,2^a*2^b>1
2^a+1/2^a-(2^b+1/2^b)>0
2^a+1/2^a>2^b+1/2^b