If $a + b + c = m$ and $a^{2} + b^{2} + c^{2} = n$ ,
then $2 (a b + b c + c a)$ is _______.

^{2}

- n

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^{2}

- m

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2m+n

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2m-n

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Solution

The correct option is A m $^{2}$ - n
Given, $a + b + c = m$ and $a^{2} + b^{2} + c^{2} = n$ .

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

$\Rightarrow$ $m^{2} = n + 2 (a b + b c + c a)$

$\Rightarrow$ $2 (a b + b c + c a) = m^{2} - n$ .

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