If (a - b)^2 + (b - c)^2 + (c - a)^2 = 6 and a^2 + b^2 + c^2 = 29, then what is (a + b + c) equal to?

Explanation

Expanding the first equation gives 2(a^2 + b^2 + c^2 - ab - bc - ca) = 6. Substituting the second gives 29 - (ab+bc+ca) = 3, so ab+bc+ca = 26. Using the identity (a+b+c)^2 = a^2+b^2+c^2 + 2(ab+bc+ca) = 29 + 2(26) = 81, we find a+b+c = \pm 9.

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