yes If the equation is symmetric in x,y then one of the solution is x=y some times this cant be solution also, so we cannot conclude that x=y with out proper argument, If we prove that there is no solution in x>y or x<y i think we can conclude x=y=-1/2 is the only solution.
any body solved please post here.
i want know how to solve this problem.
I don't want to deny you the pleasure of solving it yourself, so I'll just erect pointers.
. We want to solve
Since f is nonnegative convex and turns addition to multiplication, with
, we have
, with equality if and only if
Now what is