If A represents the arithmetic mean, H represents the harmonic mean and G represents the geometric mean, then what is the relation between them?

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Accepted Answer

A = (a + b)/2, 1/H = (1/a + 1/b)/2 ⇒ H = 2ab/(a +b), G = √ab ∴ A x H = {(a + b)/2} x {2ab/(a + b)} = ab = G2 ∴ A x H = G2

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