1st Iberoamerican Mathematical Olympiad Problems 1985

A1.  Find all integer solutions to: a + b + c = 24, a2 + b2 + c2 = 210, abc = 440. A2.  P is a point inside the equilateral triangle ABC such that PA = 5, PB = 7, PC = 8. Find AB. A3.  Find the roots r1, r2, r3, r4 of the equation 4x4 - ax3 + bx2 - cx + 5 = 0, given that they are positive reals satisfying r1/2 + r2/4 + r3/5 + r4/8 =