Question 56
Prove that for all $a,b,c\gt0$ with $a+b+c=1$,
$$
\frac1{a+bc}+\frac1{b+ca}+\frac1{c+ab}\geq\frac7{1+abc}.
$$
$$
\frac1{a+bc}+\frac1{b+ca}+\frac1{c+ab}\geq\frac7{1+abc}.
$$
MathNet 2021 — Part 10 Question 56
Math Olympiad Vault · MathNet 2021 — Part 10