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(z - x)(x - y) = a, (x - y)(y - z) = b, (y - z)(z - x) = c

Source: Polish MO Second Round 1964 p4

August 31, 2024
algebrasystem of equationsSystem

Problem Statement

Find the real numbers x,y,z x, y, z satisfying the system of equations (z−x)(x−y)=a(z - x)(x - y) = a (x−y)(y−z)=b(x - y)(y - z) = b (y−z)(z−x)=c(y - z)(z - x) = c where a,b,c a, b, c are given real numbers.
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