Answer to Question #44531 in Algebra for JASHVINDER

Question

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