MathDB

a&sup3;,b&sup3;,a+b rational, but a,b not rational

Source:

December 16, 2019

irrational numberalgebra

Problem Statement

a) Give example of two irrational numbers

a,b

having the property that

a^3,b^3,a+b

are all rational.
b) Prove that if

x,y

are two nonnegative real numbers having the property that

x^3,y^3,x+y

are rational, then

x

and

y

are both rational.
Mihai Piticari and Vladimir Cerbu