Question 177
Prove that all positive real numbers $a$, $b$ and $c$ the inequality $$
3 \leq \frac{4 a+b}{a+4 b}+\frac{4 b+c}{b+4 c}+\frac{4 c+a}{c+4 a}\lt \frac{33}{4}
$$ applies to all positive real numbers.
3 \leq \frac{4 a+b}{a+4 b}+\frac{4 b+c}{b+4 c}+\frac{4 c+a}{c+4 a}\lt \frac{33}{4}
$$ applies to all positive real numbers.