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