Question 131
Let $x, y$ be positive real numbers with $x + y = 1$, and $n$ be a positive integer with $n \ge 2$. Prove that
$$
\frac{x^n}{x+y^3} + \frac{y^n}{x^3+y} \geq \frac{2^{4-n}}{5}.
$$
$$
\frac{x^n}{x+y^3} + \frac{y^n}{x^3+y} \geq \frac{2^{4-n}}{5}.
$$