1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Putnam 1995 b4

  1. Oct 26, 2007 #1
    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. jcsd
  3. Oct 27, 2007 #2

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    They probably mean (b^2 - 2) instead of (b^2 + 2), in which case it follows from the above observation.
     
  4. Oct 27, 2007 #3
    But the "above observation" contains a quartic polynomial and in that sentence it is a quadratic. I do not understand how that transformation happened...
     
  5. Oct 27, 2007 #4

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    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?
     
  6. Oct 27, 2007 #5
    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...
     
  7. Oct 28, 2007 #6
    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?
     
  8. Oct 29, 2007 #7
    Am I right about the square root being incorrect on the linear coefficient?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Putnam 1995 b4
  1. Putnam 1951 A6 (Replies: 3)

  2. Putnam Problem 2010 A5 (Replies: 1)

Loading...