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(2): N=2 only
well it is stated in the problem that A is irrational.
Assume x=sqrt(2A+2) is rational
if x is rational then so is (x^2-2)/2 and thus so is A
which contradicts A being irrational, thus x must be irrational as well.
Posted by Daniel
on 2015-11-16 20:53:52