When I simplified the left hand side, I got
By observation you can see the the equation is true only when a = b = c. But how to prove it?
It took me quite a while to see how to simplify the left hand side to get . (It's correct, but I'll leave it to sa-ri-ga-ma to provide the details. )
So we know that . Multiply out the left side to get . Thus the equation becomes , which you can write as . That obviously only holds if .