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Lef a, b be two distinct positive numbers and A and G their arithmetic and geometric means respectively. If a, `G_(1),G_(2)`, b are in G.P. and a, `H_(1),H_(2)`, b are in H.P., prove that `(G_(1)G_(2))/(H_(1)H_(2))lt (A^(2))/(G^(2))`.

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