JAMB 1990 · UME · Q20

What must be added to $4x^2 - 4$ to make it a perfect square?

Worked solution (try it first)

Treat $-4$ as the middle term of $(2x + k)^2 = 4x^2 + 4kx + k^2$ : $4kx = -4$ , so $k = -\frac1x$ .
Then $\left(2x - \frac1x\right)^2 = 4x^2 - 4 + \frac{1}{x^2}$ .
So you must add $\frac{1}{x^2}$ , option B.