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show that the determinant |{:(a^(2)+...

show that the determinant
`|{:(a^(2)+b^(2)+c^(2),,bc+ca+ab,,bc+ca+ab),(bc+ca+ab,,a^(2)+b^(2)+c^(2),,bc+ca+ab),(bc+ca+ab,,bc+ca+ab,,a^(2)+b^(2)+c^(2)):}|`
is always non- negative.

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