Good try so far!

a, b, & c are all independent variables. Note that a & b are (positive and) arbitrarily large, which means they are not necessarily maximized when they are equal. Indeed, for any choice of a, there are infinitely many b that make ab > a*a.

But here's a hint: You can make certain choices and not alter the independence of the 3 variables.

Thanks for at least trying! You made my week. :)