Let $x$ and $y$ be real numbers where at least one of them is bigger than $2$ and $xy+4 > 2(x+y)$ holds. Show that $xy>x+y$.
Problem
Source: Kosovo Math Olympiad 2025, Grade 8, Problem 2
Tags: Inequality, Kosovo, algebra, inequalities
Source: Kosovo Math Olympiad 2025, Grade 8, Problem 2
Tags: Inequality, Kosovo, algebra, inequalities
Let $x$ and $y$ be real numbers where at least one of them is bigger than $2$ and $xy+4 > 2(x+y)$ holds. Show that $xy>x+y$.