Wednesday, November 17, 2010
3rd International Mathematical Olympiad 1961 Problems & Solutions
A1. Solve the following equations for x, y and z: x + y + z = a; x2 + y2 + z2 = b2; xy = z2. What conditions must a and b satisfy for x, y and z to be distinct positive numbers? A2. Let a, b, c be the sides of a triangle and A its area. Prove that: a2 + b2 + c2 ≥ 4√3 AWhen do we have equality? A3. Solve the equation cosnx - sinnx = 1,
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