MathDB

3

Part of 1987 USAMO

Problems(1)

If r(x),s(x) are distinct elements of $x$ then 0<x<1

Source: USAMO 1987 Problem 3

7/24/2011
Construct a set SS of polynomials inductively by the rules:
(i) x∈Sx\in S; (ii) if f(x)∈Sf(x)\in S, then xf(x)∈Sxf(x)\in S and x+(1−x)f(x)∈Sx+(1-x)f(x)\in S.
Prove that there are no two distinct polynomials in SS whose graphs intersect within the region {0<x<1}\{0 < x < 1\}.
algebrapolynomialinductionalgebra unsolved