A Chinese mathematical olympiad problem and its solution:
Some body had once commented: The Silicon Valley is full of IC’s — Indians and Chinese! .
(My humble opinion: Perhaps, because of the strong emphasis on math in the two countries.)
Solve the inequality:
As , and is monotonically increasing over , the given inequality is equivalent to :
, that is,
, which in turn, equals .
Define: . Then, we have: . Clearly, is a monotonically increasing function; then we have
That is to say, .
We obtain . So the solution set is .
Do you think you can solve this problem by another method? Please let me know.
— Nalin Pithwa.