MathDB

Find all real numbers

Source: Bulgarian IMO TST 2008, Day 1, Problem 3

July 8, 2013

functionalgebra proposedalgebra

Problem Statement

Let

\mathbb{R}^{+}

be the set of positive real numbers. Find all real numbers

a

for which there exists a function

f :\mathbb{R}^{+} \to \mathbb{R}^{+}

such that

3(f(x))^{2}=2f(f(x))+ax^{4}

, for all

x \in \mathbb{R}^{+}