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,