Prove that for any positive real numbers x, x + 1/(4x) ≥ 1.

Question

I'm stuck on this proof so any help would be greatly appreciated.

Answer 1

$x+\frac{1}{4x}\ge 1$ equivalent to $4x^2-4x+1\ge 0$ or $(2x-1)^2\ge 0$, which is true.