If $a + b + c = 5$ and $a^{2} + b^{2} + c^{2} = 29$ , then the value of $3 a b + 3 b c + 3 c a$ is

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Solution

The correct option is B $- 2$
$\begin{matrix} W e k n o w t h a t {(a + b + c)}^{2} = a^{2} + b^{2} + + c^{2} + 2 (a b + b c + c a) {(5)}^{2} = 29 + 2 (a b + b c + c a) \frac{- 4}{2} = a b + b c + c a - 2 = a b + b c + c a v a l u e o f 3 a b + 3 b c + 3 c a = 3 \times (- 2) = - 6 \end{matrix}$

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