A Law-of-Cosines System

Problem

Let $x,y,z$ be positive numbers satisfying

\begin{cases}x^2+y^2+xy=3,\\ y^2+z^2+yz=4,\\ z^2+x^2+zx=7.\end{cases}

Find $x+y+z$ .

Answer

Solution

Difficulty	8/10
Topics	Substitution, algebra, Symmetry

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