Maths Olympiad Prep

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Problem 911

AMC 12 late, AIME early
Algebra Difficulty 4.0 Find the answer BMO Round 1 · United Kingdom · 2026

Find all triples (x,y,z)(x, y, z) of real numbers satisfying the equations x2+2yz=4,y2+2zx=4,z2+2xy=1.x^2 + 2yz = 4, \qquad y^2 + 2zx = 4, \qquad z^2 + 2xy = 1.

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