If $a + b + c = 9$ and $a^{2} + b^{2} + c^{2} = 29$ ,
then $2 (a b + b c + c a)$ is ______.

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Solution

The correct option is A 52
Given, $a + b + c = 9$ and $a^{2} + b^{2} + c^{2} = 29$ .

Using the identity,
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$ ,

$\Rightarrow$ $9^{2} = 29 + 2 (a b + b c + c a)$

$\Rightarrow$ $2 (a b + b c + c a) = 9^{2} - 29$
= $81 - 29$
= $52$ .

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