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.

(In reply to N=2 only by Jer)

Which is clearly not rational if A is not rational.

It's rational if A is an integer.

It's generally, but not always, irrational if A is rational.

Does it necessarily follow that it's always irrational if A is irrational?

 

Edited on November 16, 2015, 8:18 am

Posted by broll on 2015-11-16 07:48:35