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 re: N=2 only by broll)

Isn't
Which is clearly not rational if A is not rational.
the same as
Does it necessarily follow that it's always irrational if A is irrational?


Anyhow, it seems clear to me that it follows.  How can the square root of an irrational number (2A+2) become rational (X)?

But maybe I'm wrong.  The sum/difference/product/quotient/exponents of irrationals can be rational.  Ok I've stumped myself.
(√(2)^√(2))^√(2)

Posted by Jer on 2015-11-16 20:48:21