Question

证明对任意实数a,b,有下式成立

Answer 1

1/2(e^a+e^b)-e^[(a+b)/2]

=1/2[e^a+e^b-2e^(a/2)*e^(b/2)]

=1/2(e^a+e^b-2√e^a*√e^b)

=1/2(√e^a-√e^b)²≥0

所以e^[(a+b)/2]≤1/2(e^a+e^b)