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(a + b)^2 Expansion and Visualisation

If 4x2+xm+1...

Question

If $4 x^{2} + x (m + 1) + 1$ is a perfect square, then the value of $m$ is:

- 5

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3

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Solution

The correct option is C $3$
$\Rightarrow 4 x^{2} + x (m + 1) + 1$ is a perfect square of ${(2 x + 1)}^{2}$
$\Rightarrow {(2 x + 1)}^{2} = 4 x^{2} + 4 x + 1$
then $m + 1 = 4$
$m = 4 - 1 = 3$

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