Prove inequation.i dont understand the question

if x real and p=3(x^2 + 1)/2x - 1
prove that p^2 -3(p+3) >= 0

I believe you meant to write p = 3(x^2 + 1)/(2x - 1). Parentheses are important. If you write it the way you did, then Tim is right.

If you plug the definition of p into the expression p^2 - 3(p+3) and do some algebra, you can prove that

p^2 - 3(p+3)
= [3(x^2 + 1)/(2x - 1)]^2 - 3(3(x^2 + 1)/(2x - 1) + 3)
= [3(-x^2 + x + 1)/(1-2x)]^2

This proves that p^2 - 3(p+3) is a square of a real number, so p^2 - 3(p+3) >= 0.

Think the question is badly stated....if you set x=1 which is real, p=2 and the inequality does not hold.

So it cannot be proven. Are you missing a bracket?