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

\geq (- 5 / 2)

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\geq (- 1)

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\geq 5

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Option A & C both

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Solution

The correct option is A $\geq (- 5 / 2)$
We have,
$(l + m + n)^{2} \geq 0$ as a square is always positive
$=> l^{2} + m^{2} + n^{2} + 2 (l m + m n + l n) \geq 0$
$=> 5 + 2 (l m + m n + l n) \geq 0$
$=> l m + m n + l n) \geq - \frac{- 5}{2}$

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