Algebra, fractions and numbers
Source: Polish Junior Math Olympiad 2020 Finals
October 23, 2020
algebra
Problem Statement
Let , , be non-zero real numbers, such that and the numbers
\frac{x}{y} + \frac{y}{z} + \frac{z}{x} \text{and} \frac{x}{z} + \frac{z}{y} + \frac{y}{x} + 1
are equal. Determine their common value.