equation on real numbers
Source: 2nd National Women's Contest of Mexican Mathematics Olympiad 2023 , problem 3 teams
July 23, 2023
equationalgebraMexico
Problem Statement
Find all triples of real numbers all different from zero that satisfies: \begin{eqnarray} a^4+b^2c^2=16a\nonumber \\ b^4+c^2a^2=16b \nonumber\\ c^4+a^2b^2=16c \nonumber \end{eqnarray}