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Quadratic Formula

If l2+m2+n2...

Question

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

\geq (- 5 / 2)

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\geq (- 1)

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\leq 5

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\leq 3

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Solution

The correct option is A $\geq (- 5 / 2)$
We know that
${(l + m + n)}^{2} = l^{2} + m^{2} + n^{2} + 2 (l m + m n + l n)$
$=> {(l + m + n)}^{2} = 5 + 2 (l m + m n + l n)$
We know that ${(l + m + n)}^{2}$ will be a value greater than or equal to zero
$=> {(l + m + n)}^{2} \geq 0$
$=> 5 + 2 (l m + m n + l n) \geq 0$
$=> (l m + m n + l n) \geq= \frac{5}{2}$

Suggest Corrections

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