Problem

Source: Romanian JBMO TST, Day 3, Problem 8

Tags: inequalities, inequalities proposed, highschoolmath



Let $a$, $b$, $c$ be three positive reals such that $(a+b)(b+c)(c+a)=1$. Prove that the following inequality holds: \[ ab+bc+ca \leq \frac 34 . \] Cezar Lupu