We are looking for
where
under the restriction
.
Hence, we set
, therefore it suffices to find
.
Considering the symmetricity, and it suffices to examine the partial derivative of
with respect to
.
It follows that the critical points are
and
.
Clearly,
.
On the other hand, let
We find that the critical point for
is
, and
, which is the max value of
(at
) at the same time because the other critical point
makes
attain
.
Therefore, the given inequality holds.
Not. I know this is a long solution and not so nice. :S