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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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Some Thoughts N=2 only | Comment 1 of 6
I don't know yet if this will generalize to all N, but if N=2:

X=√(A + √(A2-1)) + √( A - √(A2-1))

X^2 = (A + √(A2-1)) +2√(A + √(A2-1)( A - √(A2-1)) +( A - √(A2-1))
X^2= 2A+2√(A2 - (A2-1))
X^2= 2A+2

X=√(2A+2)
Which is clearly not rational if A is not rational.

  Posted by Jer on 2015-11-16 07:26:45
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