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Which is greater? (Posted on 2016-08-28) Difficulty: 3 of 5
Each of A and B is a positive real number and N is an integer with N > 1 satisfying:
AN - A - 1 = 0, and:
B2N - B – 3A = 0

Which of A and B is greater?

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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Some Thoughts Suspicion | Comment 2 of 3 |
Based on Charlie's work, I suspect that A > B for all N.

We know that A never equals B, because,
The first equation is A^N = A + 1
The second is B^2N = B + 3A.

Squaring the first and subtracting the 2nd gives
A^2n - B^2N = A^2 + -A - B + 1

If A = B they we have 0 = A^2 - 2A +1

This leads to A = 1, but this violates equation 1.



  Posted by Steve Herman on 2016-08-28 20:49:52
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