System of equations
Source: Latvian TST for Baltic Way 2021 P3
September 25, 2021
algebrasystem of equations
Problem Statement
Find all triplets of real numbers such that the following equations are satisfied simultaneously:
\begin{align*}
x^3+y=z^2 \\
y^3+z=x^2 \\
z^3+x =y^2
\end{align*}