# Not $$x = y = z$$

Algebra Level 5

$\large\dfrac{x^3+y^3+z^3}{(x+y+z)(x^2+y^2+z^2)}$

Let $$x, y, z$$ be non-negative real numbers such that $$x^2+y^2+z^2=2(xy+yz+zx)$$. Find the maximum value of the expression above.