1995 OIM Problems/Problem 2

Problem

Let $n$ be an integer greater than 1. Find the real numbers

$X_1, X_2, \cdots ,X_n \ge 1,\;\text{and}\; X_{n+1} > 0$

that verify the following two conditions:

a. $X_1^{1/2} + X_2^{3/2} + \cdots + X_n^{n+1/2} = n.X_{n+1}^{1/2}$

b. $(X_1 + X_2 + \cdots + X_n)/n = X_{n+1}$

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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