Question 23
Given that the sequence of positive numbers $\{a_n\}$ satisfies the conditions that
$$a_{n+1}=\frac{a_n^2+1}{2a_n-1},\quad\forall n\ge1$$
and $a_{2025}=\sqrt{1+\sqrt{1+a_{2025}}}$, determine the value of $a_1^2-a_1$.
$$a_{n+1}=\frac{a_n^2+1}{2a_n-1},\quad\forall n\ge1$$
and $a_{2025}=\sqrt{1+\sqrt{1+a_{2025}}}$, determine the value of $a_1^2-a_1$.