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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(2): N=2 only | Comment 3 of 6 |
(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 2015-11-16 20:48:21
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