Question 5
Determine all pairs of real numbers $a,b$ such that for every positive integer $n$ and every real solution $x_n$ of
$$4n^2x=\log_2(2n^2x+1),$$
one has
$$a^{x_n}+b^{x_n}\ge2+3x_n.$$
The powers and the logarithm must be defined as real numbers.
The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.
$$4n^2x=\log_2(2n^2x+1),$$
one has
$$a^{x_n}+b^{x_n}\ge2+3x_n.$$
The powers and the logarithm must be defined as real numbers.
The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.