Please turn on javascript in your browser to play chess.
Posers and Puzzles

Posers and Puzzles

  1. Standard member royalchicken
    05 Dec '04 08:55 / 1 edit
    Not mine:

    If t1,t2, are positive reals for some integer n and:

    (t1+t2+...+tn)(1/t1 + 1/t2 +...+1/tn) < n^2+1

    prove that any three distinct ti, tj, tk are side lengths of a triangle.

    It's a good idea to look at the case n=3 first, since it's much more obvious and you can see how it works.