MathDB
x/y + y/z + z/x = x/z + z/y + y/x , x^2 + y^2 + z^2 = xy + yz + zx + 4

Source: 2021 Czech-Polish-Slovak Match Junior, team p5 CPSJ

September 12, 2021
algebrasystem of equations

Problem Statement

Find all three real numbers (x,y,z)(x, y, z) satisfying the system of equations xy+yz+zx=xz+zy+yx\frac{x}{y}+\frac{y}{z}+\frac{z}{x}=\frac{x}{z}+\frac{z}{y}+\frac{y}{x} x2+y2+z2=xy+yz+zx+4x^2 + y^2 + z^2 = xy + yz + zx + 4
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