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Irrational Decision (Posted on 2015-11-15) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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re(3): N=2 only | Comment 4 of 6 |
(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
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
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