MathDB

P3

Part of 2021 Latvia Baltic Way TST

Problems(1)

System of equations

Source: Latvian TST for Baltic Way 2021 P3

9/25/2021
Find all triplets of real numbers (x,y,z)(x,y,z) 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*}
algebrasystem of equations