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MathNet 2009-part-04 — 175 problems (EN–VI) Question 122

Math Olympiad Vault · MathNet 2009-part-04 — 175 problems (EN–VI)

Question 122

For which values of parameter $a$ the system of equations
$$
\begin{cases} x + y + z = 0 \\ (xy + yz) + a xz = 0 \end{cases} \text{ has a unique solution?}
$$