perplexus.info :: Just Math : Which is greater?

Which is greater? (Posted on 2016-08-28)

Each of A and B is a positive real number and N is an integer with N > 1 satisfying:
A^N - A - 1 = 0, and:
B^2N - B – 3A = 0

Which of A and B is greater?

See The Solution Submitted by K Sengupta

Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

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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