parmenides51 wrote: Let $a, b, c$ be positive real numbers with $abc = 1$. Prove that $$1 + \frac{3}{a+b+c}\ge \frac{6}{ab+bc+ca}$$ https://artofproblemsolving.com/community/c6h14765p104748 Let $a,b$ and $c$ be positive real numbers. Prove that $$1+\frac{3}{ab+bc+ca}\geq \frac{6}{a+b+c}.$$