Question 181
Let $n$ be a given positive integer. Solve the system of equations
$$
\begin{aligned}
x_1 + x_2^2 + x_3^3 + \dots + x_n^n &= n, \\
x_1 + 2x_2 + 3x_3 + \dots + nx_n &= \frac{n(n+1)}{2}
\end{aligned}
$$
in the set of nonnegative real numbers $x_1, x_2, \dots, x_n$.
$$
\begin{aligned}
x_1 + x_2^2 + x_3^3 + \dots + x_n^n &= n, \\
x_1 + 2x_2 + 3x_3 + \dots + nx_n &= \frac{n(n+1)}{2}
\end{aligned}
$$
in the set of nonnegative real numbers $x_1, x_2, \dots, x_n$.