Aha!So, after much helpful advice...First rearrange the given equation to 4(3F – H)^{2} + (3F - 2G)^{2} + 9(H – 2G)^{2} = 0then deduce that 3F = 2G = H, so any triple must be of the form (f, 3f/2, 3f).Substitution into the equation 1/F + 1/G + 1/H = 1 then givesf = 1 + 2/3 + 1/3 = 2, so the only possible triple is (2, 3, 6).
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