# Answer on Algebra Question 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.]

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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