MathDB

Centroamerican Olympiad 2010, problem 5

Source:

May 30, 2010

algebrapolynomialinequalitiestriangle inequalityalgebra proposed

Problem Statement

p

q

and

r

are nonzero rational numbers such that

\sqrt[3]{pq^2}+\sqrt[3]{qr^2}+\sqrt[3]{rp^2}

is a nonzero rational number, prove that

\frac{1}{\sqrt[3]{pq^2}}+\frac{1}{\sqrt[3]{qr^2}}+\frac{1}{\sqrt[3]{rp^2}}

is also a rational number.