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Answer to Question #45629 in Algebra for vimal

Question #45629
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.]
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