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System of equations with powers

Source: Latvian TST for Baltic Way 2022 P1

October 25, 2022
algebrasystem of equations

Problem Statement

Find all triplets of positive real numbers (x,y,z)(x,y,z) that satisfy the following system of equations: {x+y2+z3=3y+z2+x3=3z+x2+y3=3. \begin{cases} x+y^2+z^3=3\\ y+z^2+x^3=3\\ z+x^2+y^3=3. \end{cases}
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