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MathNet 2009-part-03 — 175 problems (EN–VI) Question 38

Math Olympiad Vault · MathNet 2009-part-03 — 175 problems (EN–VI)

Question 38

Solve the system of equations
$$
\begin{cases}
x + y = z \\
x^2 + y^2 = z \\
x^3 + y^3 = z
\end{cases}
$$