*Problem:*

If it holds that , then find the value of

.

*1st solution:*

From the Power-Mean Inequality we have that

.

So, multiplying by we have that

.

Taking now in hand the left hand side, we know that

.

So, we know that . Doing the manipulations on both sides we get that

, hence ,* Q.E.D.*

*2nd solution (An idea by Vo Quoc Ba Can):*

The inequality is symmetric on . So, we only need to find the maximum of those two constants for the values of which

, that is . S

o, plugging on the above inequality the value

we get the desired maximum result, *Q.E.D.*