AUSTRIAN-POLISH 1990 Problem 3

Show that there are two real solutions to: $\begin{cases} x + y^2 + z^4 = 0 y + z^2 + x^4 = 0 z + x^2 + y^5 = 0\end {cases}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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