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1. $a^{2} + b^{2} + c^{2}$

Answer: Option A

Explanation:

w e k n o w, a^{2} + b^{2} + c^{2} = (a + b + c)^{2} - 2 a b - 2 b c - 2 c a = > 83 = (15)^{2} - 2 (a b + b c + c a) [V a l u e] = > 83 = 225 - 2 (a b + b c + c a) = > 83 - 225 = - 2 (a b + b c + c a) = > - 142 = - 2 (a b + b c + c a) = > \frac{142}{2} = (a b + b c + c a) = > 71 = (a b + b c + c a) (a b + b c + c a) = 71

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