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x^2+xy+y^2=57, y^2+yz+z^2=84, z^2+zx+x^2=111

Source: Mathcenter Contest / Oly - Thai Forum 2008 R1 p1 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 10, 2022
algebrasystem of equationsSystem

Problem Statement

Given x,y,zāˆˆR+x,y,z\in \mathbb{R} ^+ , that are the solutions to the system of equations : x2+xy+y2=57x^2+xy+y^2=57 y2+yz+z2=84y^2+yz+z^2=84 z2+zx+x2=111z^2+zx+x^2=111 What is the value of xy+3yz+5zxxy+3yz+5zx?
(maphybich)
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