VN-TST 1997 Problem 5

Find all pairs of positive real numbers $(a, b)$ such that for every $n \in\mathbb{N}^*$ and every real root $x_n$ of the equation $4n^2x = \log_2(2n^2x + 1)$ we always have $a^{x_n} + b^{x_n} \ge 2 + 3x_n$ .