Question 78
Solve, in real numbers, the system
$$
\begin{aligned}
x + \frac{1}{y} = y + \frac{1}{z} = z + \frac{1}{x} \\
xyz = 1
\end{aligned}
$$
$$
\begin{aligned}
x + \frac{1}{y} = y + \frac{1}{z} = z + \frac{1}{x} \\
xyz = 1
\end{aligned}
$$
MathNet 2009-part-01 — 175 problems (EN–VI) Question 78
Math Olympiad Vault · MathNet 2009-part-01 — 175 problems (EN–VI)