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.
I don't know yet if this will generalize to all N, but if N=2:
X=√(A + √(A^{2}1)) + √( A  √(A^{2}1))
X^2 = (A + √(A^{2}1)) +2√(A + √(A^{2}1)( A  √(A^{2}1)) +( A  √(A^{2}1))
X^2= 2A+2√(A^{2}  (A^{2}1))
X^2= 2A+2
X=√(2A+2)
Which is clearly not rational if A is not rational.

Posted by Jer
on 20151116 07:26:45 