Find the value of p if the expression px^2-3÷2x+1÷16 is a perfect square ,given that p is constant

Answer 1

Let's start by considering the expression (2x+1)^2 and expanding it:

(2x+1)^2 = 4x^2+4x+1

We can rewrite this as:

4x^2+4x+1 = (4x^2+8x+4) - (4x+3) + 1

= 4(x+1)^2 - (4x+3)

So we can see that if p=4, then px^2-3÷2x+1÷16 will be equal to (2x+1)^2. Therefore, if p=4, the expression would be a perfect square.

Therefore, the value of p is 4.