Funny system of equations in three variables
Source: Baltic Way 2020, Problem 5
November 14, 2020
algebrasystem of equationsalgebra proposed
Problem Statement
Find all real numbers so that
\begin{align*}
x^2 y + y^2 z + z^2 &= 0 \\
z^3 + z^2 y + z y^3 + x^2 y &= \frac{1}{4}(x^4 + y^4).
\end{align*}