MathDB

5

Part of 2006 Junior Tuymaada Olympiad

Problems(1)

trinomials f,g,h are sides of a triangle, but f(x)-1,g(x) -1, h(x) -1 are not

Source: Tuymaada Junior 2006 p5

5/12/2019
The quadratic trinomials f f , g g and h h are such that for every real x x the numbers f(x) f (x) , g(x) g (x) and h(x) h (x) are the lengths of the sides of some triangles, and the numbers f(x)−1 f (x) -1 , g(x)−1 g (x) -1 and h(x)−1 h (x) -1 are not the lengths of the sides of the triangle. Prove that at least of the polynomials f+g−h f + g-h , f+h−g f + h-g , g+h−f g + h-f is constant.
algebraquadratic trinomialtrinomialquadraticsconstantSides of a triangle