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Algebraic Identities

IF a2 + b2 +c...

Question

IF $a^{2} + b^{2} + c^{2} = 250$ and $a b + b c + c a = 3,$ find a + b +c.

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Solution

$a^{2} + b^{2} + c^{2} = 250, a b + b c + c a = 3 (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a) = 250 + 2 \times 3 = 250 + 6 = 256 = (\pm 16)^{2} ∴ a + b + c = \pm 16$

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