1961 IMO Problems
(Hungary) Solve the system of equations:
where and are constants. Give the conditions that and must satisfy so that (the solutions of the system) are distinct positive numbers.
Let a,b, and c be the lengths of a triangle whose area is S. Prove that
In what case does equality hold?
Solve the equation
where n is a given positive integer.
In the interior of triangle a point P is given. Let be the intersections of with the opposing edges of triangle . Prove that among the ratios there exists one not larger than 2 and one not smaller than 2.