If $4 l^{2} + (k + 10) l m + 25 m^{2}$ is a perfect square, then the value of $k$ is _________.

- 9

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

10

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

0

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

5

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

Open in App

Solution

The correct option is B $10$
Let given expression is a perfect square
$4 l^{2} + (k + 10) l m + 25 m^{2} = (2 l + 5 m)^{2}$
$\Rightarrow 4 l^{2} + (k + 10) l m + 25 m^{2} = 4 l^{2} + 25 m^{2} + 2 \times 2 l \times 5 m$
$\Rightarrow (k + 10) l m = 20 l m$
$\Rightarrow k + 10 = 20$
$\Rightarrow k = 10$

Suggest Corrections

Similar questions

(x + 1) (x + 2) (x + 3) (x + k) + 1

For what value of $k, (4 - k) x^{2} + (2 k + 4) x + (8 k + 1) = 0$ , is a perfect square.

4 l^{2} - 5 m^{2} + 6 l + 1 = 0

l x + m y + 1 = 0

x^{2} + y^{2} - 6 x + k = 0

k

k

4 x^{2} - k x + 9

k

{4 x}^{2} - k x + 9

Join BYJU'S Learning Program