MathNet 2026 — Part 04 Question 109

Show that if $a, b, c$ are positive real numbers checking $a+b+c=1$ then $$
\frac{7+2 b}{1+a}+\frac{7+2 c}{1+b}+\frac{7+2 a}{1+c} \geqslant \frac{69}{4}
$$