Question 38
Let $x, y$ be distinct positive numbers, and let $n$ be a positive integer greater than 1. If
$$
x^n - y^n = x^{n+1} - y^{n+1},
$$
prove that
$$
1 \lt x + y \lt \frac{2n}{n + 1}.
$$
$$
x^n - y^n = x^{n+1} - y^{n+1},
$$
prove that
$$
1 \lt x + y \lt \frac{2n}{n + 1}.
$$