Problem

Source: Romanian JBMO TST 2006, Day 3, Problem 3

Tags: trigonometry, inequalities, algebra, High school olympiad



Find all real numbers $ a$ and $ b$ such that \[ 2(a^2 + 1)(b^2 + 1) = (a + 1)(b + 1)(ab + 1). \] Valentin Vornicu