MathDB

Both numbers are rational

Source: Greece JMO 2018, pr1

March 5, 2018

rational numberalgebra

Problem Statement

a) Does there exist a real number

x

such that

x+\sqrt{3}

and

x^2+\sqrt{3}

are both rationals? b) Does there exist a real number

y

such that

y+\sqrt{3}

and

y^3+\sqrt{3}

are both rationals?