Problem

Source: andrei ciupan

Tags: inequalities, inequalities proposed



Let $a, b, c$ three positive reals such that \[\frac{1}{a+b+1}+\frac{1}{b+c+1}+\frac{1}{c+a+1}\geq 1. \] Show that \[a+b+c\geq ab+bc+ca. \]