Let x,y,z be non-negative real numbers satisfying the condition x+y+z=1 . The maximum possible value of x^3*y^3+y^3*z^3+z^3*x^3 has the form a/b where a and b are positive, coprime integers. What is the value of a+b ?

Answer 1

wolframalpha says that the maximum is at (1/3,1/3,1/3)

So, f(x,y,z) is 1/243

Answer 2

wrong there is other max but wolfram dpoesnt give excct val