Question 152
Let be given positive numbers $a, b, c$. Prove that:
$$
\frac{a}{2a^2 + b^2 + c^2} + \frac{b}{2b^2 + c^2 + a^2} + \frac{c}{2c^2 + a^2 + b^2} \le \frac{9}{4(a+b+c)}
$$
$$
\frac{a}{2a^2 + b^2 + c^2} + \frac{b}{2b^2 + c^2 + a^2} + \frac{c}{2c^2 + a^2 + b^2} \le \frac{9}{4(a+b+c)}
$$