For positive numbers $a, b, c$ holds $(a + c) (b^2 + a c) = 4a$. Determine the maximum value of $b + c$ and find all triplets of numbers $(a, b, c)$ for which expression takes this value
Problem
Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 2016 p4
Tags: inequalities, maximum value, maximum, algebra