4

Part of 1977 Czech and Slovak Olympiad III A

Problems(1)

System of symmetric equations

Source: Czech and Slovak Olympiad 1977, National Round, Problem 4

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*}

algebrasystem of equationssymmetry