Given a in RR^+, a ne 1 and n in NN, n > 1 Prove that n^2 < (a^n + a^(-n)-2)/(a+a^(-1)-2)?
2 Answers
Let a > 1. Then
, using
Likewise, when a < 1,
, using
So, the given expression is
then
with
This is a continuous even function having a minimum at
also we have
so the proof follows.