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3x3 system x^5 = 2y^3 + y - 2, y^5 = 2z^3 + z - 2, z^5 = 2x^3 + x - 2

Source: 2010 Indonesia TST stage 2 test 5 p1

December 16, 2020
algebrasystem of equations

Problem Statement

Find all triplets of real numbers (x,y,z)(x, y, z) that satisfies the system of equations x5=2y3+y−2x^5 = 2y^3 + y - 2 y5=2z3+z−2y^5 = 2z^3 + z - 2 z5=2x3+x−2z^5 = 2x^3 + x - 2
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