Question 51
Consider the polynomial $P(x) = x^2 - 1$. Let $a$ be a real number satisfying
$$P(P(P(a))) = 2024.$$
Write the value of $a^2$ as $m + \sqrt{n}$, where $m, n$ are positive integers and $n$ is not divisible by any perfect square greater than $1$. Then the value of $m+n$ is $\underline{\qquad}$.
$$P(P(P(a))) = 2024.$$
Write the value of $a^2$ as $m + \sqrt{n}$, where $m, n$ are positive integers and $n$ is not divisible by any perfect square greater than $1$. Then the value of $m+n$ is $\underline{\qquad}$.