You visited us 1 times! Enjoying our articles? Unlock Full Access!

Quadratic Formula

If l2+m2+n2...

Question

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

\geq (- 5 / 2)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\geq (- 1)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\leq 5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\leq 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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

Similar questions

l^{2} + m^{2} + n^{2} = 5,

(l m + m n + l n)

l^{2} + m^{2} + n^{2} = 5

(l m + m n + l n)

(i) m - n, m + n

(i i) m n + 5 - 2, m n + 3

θ

\frac{2}{7}, \frac{3}{7}, - \frac{6}{7}

\frac{3}{5 \sqrt{2}}, \frac{- 4}{5 \sqrt{2}}, \frac{5}{5 \sqrt{2}}

{cos}^{- 1} (\frac{- 36}{35 \sqrt{2}})

θ

l_{1}, m_{1}, n_{1}

l_{2}, m_{2}, n_{2}

cos θ = l_{1} l_{2} + m_{1} m_{2} + n_{1} n_{2}

m^{2} + {m^{'}}^{2} + 2 m m^{'} cos θ = 1

n^{2} + {n^{'}}^{2} + 2 n n^{'} cos θ = 1

m n + m^{'} n^{'} + (m n^{'} + m^{'} n) = cos θ = θ

m^{2} + n^{2} = {csc}^{2} θ

Join BYJU'S Learning Program