Let A be an irrational number and let N is an integer > 1.
Is ^{N}√(A + √(A^{2}1)) + ^{N}√( A  √(A^{2}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)?
X=√(2A+2)
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 20151116 20:48:21 