Let a, B, C be any integer which is not completely equal, if x = A2 BC, y = B2 AC, z = C2 ab
It is proved that: suppose x, y, Z are all less than 0, ∵ x = A2 BC, y = B2 Ca, z = C2 AB, ∵ 2 (x + y + Z) = 2a2-2bc + 2b2-2ca + 2c2-2ab = (a2-2ab + B2) + (b2-2bc + C2) + (a2-2ca + C2) = (a-b) 2 + (B-C) 2 + (C-A) 2 < 0, ∵ this is the same as (a-b) 2 + (B-C) 2 + (C-A) 2 ≥ 0
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