Let $a$ and $b$ be two positive real numbers such that $a^{2007} = a + 1$ and $b^{4014} = b + 3a$. Determine whether $a > b$ or $b > a$.
Source: Indian Postal Coaching 2007 set 6 p3
Tags: algebra, inequalities
Let $a$ and $b$ be two positive real numbers such that $a^{2007} = a + 1$ and $b^{4014} = b + 3a$. Determine whether $a > b$ or $b > a$.