# Putnam 1995 b4

1. Oct 26, 2007

### ehrenfest

1. The problem statement, all variables and given/known data
Here is the problem:
http://www.unl.edu/amc/a-activities/a7-problems/putnam/-pdf/1995.pdf [Broken]

Here is the solution:
http://www.unl.edu/amc/a-activities/a7-problems/putnam/-pdf/1995s.pdf [Broken]

In the solution, I am not sure why the sentence that starts (ironically) with "Clearly, then" is true?

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 3, 2017
2. Oct 27, 2007

### morphism

They probably mean (b^2 - 2) instead of (b^2 + 2), in which case it follows from the above observation.

3. Oct 27, 2007

### ehrenfest

But the "above observation" contains a quartic polynomial and in that sentence it is a quadratic. I do not understand how that transformation happened...

4. Oct 27, 2007

### morphism

Right, but do you notice anything special about the above quartic? Try setting y=x^2. Do you see the relevance of the phrase "positive square roots" now?

5. Oct 27, 2007

### ehrenfest

I know I am missing something really obvious, but if you set y = x^2, you get

y^2 - (b^2-1)y+1 = 0

I am not sure where the sqrt of the linear coefficient comes from...

6. Oct 28, 2007

### ehrenfest

I see. The square root of the linear coefficient should not be there! Also, when they say positive square roots they mean the squares of the positive roots, right?

7. Oct 29, 2007

### ehrenfest

Am I right about the square root being incorrect on the linear coefficient?