All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Irrational Decision (Posted on 2015-11-15) Difficulty: 3 of 5
Let A be an irrational number and let N is an integer > 1.

Is N√(A + √(A2-1)) + N√( A - √(A2-1)) always an irrational number?

Give reasons for your answer.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re(3): N=2 only | Comment 4 of 6 |
(In reply to re(2): N=2 only by Jer)

well it is stated in the problem that A is irrational.


Assume x=sqrt(2A+2) is rational
then
x^2=2A+2
A=(x^2-2)/2
if x is rational then so is (x^2-2)/2 and thus so is A
which contradicts A being irrational, thus x must be irrational as well.

  Posted by Daniel on 2015-11-16 20:53:52
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information