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