System of symmetric equations
Source: Czech and Slovak Olympiad 1977, National Round, Problem 4
October 10, 2024
algebrasystem of equationssymmetry
Problem Statement
Determine all real solutions of the system
\begin{align*}
x+y+z &=3, \\
\frac1x+\frac1y+\frac1z &= \frac{5}{12}, \\
x^3+y^3+z^3 &=45.
\end{align*}