For every positive $a, b, c, d$ such that $a + c\le ac$ and $b + d \le bd$ prove that $ab + cd \ge 8$.
Problem
Source: Kyiv mathematical festival 2013
Tags: Inequality, 4-variable inequality, inequalities, algebra
Source: Kyiv mathematical festival 2013
Tags: Inequality, 4-variable inequality, inequalities, algebra
For every positive $a, b, c, d$ such that $a + c\le ac$ and $b + d \le bd$ prove that $ab + cd \ge 8$.