MathDB
A nice system of equations

Source: Greece National Olympiad 2023, Problem 1

February 19, 2023
algebrasystem of equations

Problem Statement

Find all quadruplets (x, y, z, w) of positive real numbers that satisfy the following system: {xyz+1x+1=yzw+1y+1=zwx+1z+1=wxy+1w+1x+y+z+w=48\begin{cases} \frac{xyz+1}{x+1}= \frac{yzw+1}{y+1}= \frac{zwx+1}{z+1}= \frac{wxy+1}{w+1}\\ x+y+z+w= 48 \end{cases}
Back to ProblemsView on AoPS