Inequality proof with sequences - showing $x_n<x_{n+1}$ for $x_{n+1}=x_n^2 + 1/4$, $x<1/2$

Question

So I was doing part 2 of this question and I wanted to know if my approach is correct.

$x_{n+1} - x_n = x_n^2 + 1/4 - x_n$

Now since it is a sequence of positive terms $x_n$ > 0

Therefore $x_n^2 + 1/4 > 1/4 > x_n$

Hence $x_n^2 + 1/4 - x_n > 0$

$x_{n+1} - x_n > 0$

$x_n < x_{n+1}$

Answer 1

(i).

Because by assumption of the induction $$x_{n+1}=x_n^2+\frac{1}{4}<\frac{1}{4}+\frac{1}{4}=\frac{1}{2}.$$

$(ii).$

$$x_{n+1}-x_n=x_n^2-x_n+\frac{1}{4}=\left(x_n-\frac{1}{2}\right)^2>0.$$