MathDB

5

Part of 2020 Baltic Way

Problems(1)

Funny system of equations in three variables

Source: Baltic Way 2020, Problem 5

11/14/2020
Find all real numbers x,y,zx,y,z 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*}
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