KöMaL 2019 C1532

Show that if $a$ , $b$ , $c$ are positive numbers and $a+b+c\ge\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ac},$ then one of them is at least 1.

Official text KöMaL. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.