HMMT November 2013 U27

Find all triples of real numbers $(a, b, c)$ such that $a^{2}+2 b^{2}-2 b c=16$ and $2 a b-c^{2}=16$ .

Dataset text NuminaMath olympiads. Quoted with source.

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(4,4,4),(-4,-4,-4)

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