4th Iberoamerican Mathematical Olympiad Problems 1989

A1.  Find all real solutions to: x + y - z = -1; x2 - y2 + z2 = 1, -x3 + y3 + z3 = -1. A2.  Given positive real numbers x, y, z each less than π/2, show that π/2 + 2 sin x cos y + 2 sin y cos z > sin 2x + sin 2y + sin 2z. A3.  If a, b, c, are the sides of a triangle, show that (a - b)/(a + b) + (b - c)/(b + c) + (c - a)/(a + c) < 1/16.

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