Find all triples $(x,y,z)$ of positive real numbers such that $$ \begin{cases} 2x^2+y^3=3 \\ 3y^2+z^3=4 \\ 4z^2+x^3=5 \\ \end{cases} $$M. Zorka
Source: Belarusian National Olympiad 2024
Tags: algebra, system of equations
Find all triples $(x,y,z)$ of positive real numbers such that $$ \begin{cases} 2x^2+y^3=3 \\ 3y^2+z^3=4 \\ 4z^2+x^3=5 \\ \end{cases} $$M. Zorka