If $l^{2} + m^{2} + n^{2} = 5$ then $(l m + m n + l n)$ is:

\geq

\frac{- 5}{2}

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\geq (- 1)

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\leq 5

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Option A & C both

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Solution

The correct option is A $\geq$ $\frac{- 5}{2}$
$l^{2} + m^{2} + n^{2} = 5$
Now, we know
$(l + m + n)^{2} = l^{2} + m^{2} + n^{2} + 2 (l m + m n + n l)$
Since $(l + m + n)^{2} \geq 0$ square of a term is laways positive
$l^{2} + m^{2} + n^{2} + 2 (l m + m n + n l) \geq 0$
$2 (l m + n m + n l) \geq - 5$
$(l m + m n + n l) \geq \frac{- 5}{2}$

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