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(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^22)/2
if x is rational then so is (x^22)/2 and thus so is A
which contradicts A being irrational, thus x must be irrational as well.

Posted by Daniel
on 20151116 20:53:52 