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Math Help - equation

  1. #1
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    Smile equation

    Hey guys, I have some math homework...
    The last equation I can't solve is that:

    (x^2+x+1)^2(x^2-x+1)=3

    Please help me solve that one
    Thanks!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by dgolverk
    Hey guys, I have some math homework...
    The last equation I can't solve is that:

    (x^2+x+1)^2(x^2-x+1)=3

    Please help me solve that one
    Thanks!
    Expanded out your equation is:
    x^6+x^5+2x^4+x^3+2x^2+x-2=0

    Using the rational roots test the possible rational zeros are x = +/- 1, +/- 2. The only rational solution is x = -1. Using synthetic division on the zero x = -1 gives:
    x^5+2x^3-x^2+3x-2=0
    which does have a real solution near x = 0.611 (so the other 4 are complex), but being a 5th degree polynomial equation I don't have a way to generally solve it exactly.

    -Dan
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  3. #3
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    Isn't there other way?
    It's somehow supposed to be related to quadratic equations or something.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by dgolverk
    Isn't there other way?
    It's somehow supposed to be related to quadratic equations or something.
    There may be a trick involved. I noted when I looked at the problem that each factor is related to the factorization of the sum and difference of two cubes:
    x^3 - 1 = (x-1)(x^2+x+1)
    and
    x^3+1=(x+1)(x^2-x+1)

    However, I can't think of a way to use this information. That 3 on the RHS spoils things pretty badly for me. Sorry!

    -Dan
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  5. #5
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    I see...thanks anyway
    someone else can help?
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