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Polynomials math problem

  1. Jan 15, 2012 #1
    1. The problem statement, all variables and given/known data
    Find [tex]x[/tex]
    [tex](17-x)^2(11-x)+256-32(17-x)-64(11-x)=0[/tex]


    2. Relevant equations



    3. The attempt at a solution
    This eq has 3 solutions. I solved this by multiplication. Is this some other easier way. Perhaps to group some of the factors [tex]17-x[/tex] and [tex]11-x[/tex]. Tnx for the answer.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 15, 2012 #2

    SammyS

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    Staff Emeritus
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    Re: Polynomials

    I don't know of any particularly easy way. When multiplied out you have some pretty big coefficients and a very large constant term.

    Use some substitution. Either of the following is suggested by the problem itself.
    [itex]u=17-x[/itex]

    [itex]v=11-x[/itex]​
    The first takes a little less computation. It results in:
    [itex]u^3-6u^2-96u+640=0[/itex]​
    The other results in a much smaller constant term.
    [itex]v^3+12v^2-60v+64=0[/itex]​

    Of course if you use the substitution, [itex]t=9-x\,,[/itex] you get a very simple polynomial.
     
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