Question 141
Let $x_1, x_2, \dots, x_5$ be nonnegative real numbers with $\sum_{i=1}^5 \frac{1}{1+x_i} = 1$.
Prove that $\sum_{i=1}^5 \frac{x_i}{4+x_i^2} \le 1$. (posed by Li Shenghong)
Prove that $\sum_{i=1}^5 \frac{x_i}{4+x_i^2} \le 1$. (posed by Li Shenghong)