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x+y+z=x^2+y^2+z^2+18xyz=1

Source: Mathcenter Contest / Oly - Thai Forum 2011 (R1) p5 sl-6 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 14, 2022
algebrasystem of equationsSystem

Problem Statement

Given x,y,zāˆˆR+x,y,z\in \mathbb{R^+}. Find all sets of x,y,zx,y,z that correspond to x+y+z=x2+y2+z2+18xyz=1x+y+z=x^2+y^2+z^2+18xyz=1 (Zhuge Liang)
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