December 23rd, 2017, 04:05 AM  #1 
Senior Member Joined: Dec 2015 From: somewhere Posts: 514 Thanks: 80  Irrational numbers
Find the two irrational numbers $\displaystyle (\alpha,\beta)$ such that $\displaystyle \alpha^2  \beta \in N $

December 23rd, 2017, 04:24 AM  #2 
Senior Member Joined: Sep 2016 From: USA Posts: 609 Thanks: 378 Math Focus: Dynamical systems, analytic function theory, numerics 
$\alpha = \sqrt{\sqrt{2}+2}, \beta = 1 + \sqrt{2}$

December 23rd, 2017, 04:24 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,660 Thanks: 2635 Math Focus: Mainly analysis and algebra 
It's not "the two irrational numbers", there are an infinity of them. One suggestion: what if $\beta$ is a solution of, for example, $x^2x1=0$ (there are infinitely many other quadratics that would work). 

Tags 
irrational, numbers 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
irrational numbers  jeho  Number Theory  5  October 8th, 2016 05:59 AM 
Prime numbers and irrational numbers  Pengkuan  Math  61  February 29th, 2016 04:46 PM 
irrational numbers  Albert.Teng  Algebra  4  February 12th, 2014 04:55 PM 
Irrational numbers  niki500  Number Theory  5  October 7th, 2012 09:10 PM 
Irrational Numbers  Mighty Mouse Jr  Algebra  1  October 16th, 2010 07:46 PM 