Question 30
Do positive real numbers $x, y, z$ have to be equal, if they satisfy
$$
\frac{xy + 1}{x + 1} = \frac{yz + 1}{y + 1} = \frac{zx + 1}{z + 1}
$$
$$
\frac{xy + 1}{x + 1} = \frac{yz + 1}{y + 1} = \frac{zx + 1}{z + 1}
$$
MathNet 2021 — Part 09 Question 30
Math Olympiad Vault · MathNet 2021 — Part 09