Question

Let m, n, x, y, z be positive real numbers, with x + y + z = 1. Prove that
(x^4)/(mx+ny)(my+nx) + (y^4)/(my+nz)(mz+ny) + (z^4)/(mz+nx)(mx+nz) is greater than or equal to 1/3(m+n)^2
[Hint: Apply the AM ≥ GM inequality to each term in the LHS, and then apply the CS
inequality.]