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Math Help - How should I solve this?

  1. #1
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    How should I solve this?

    Solve: x^4-2x^3-2x-1=0

    I got the right solution, but I don't think I went about it the right way... I think I just had a lucky guess. How would you solve this?
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  2. #2
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    hint

    x^4-2x^3-2x-1=x^4-2x^3-x^2+x^2-2x-1=(x^4-2x^3-x^2)+(x^2-2x-1)
    Can you proceed from here?

    --Kevin C.
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  3. #3
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    Quote Originally Posted by TwistedOne151 View Post
    x^4-2x^3-2x-1=x^4-2x^3-x^2+x^2-2x-1=(x^4-2x^3-x^2)+(x^2-2x-1)
    Can you proceed from here?

    --Kevin C.
    How did you know which x^2 to pick?
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  4. #4
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    Quote Originally Posted by TwistedOne151 View Post
    x^4-2x^3-2x-1=x^4-2x^3-x^2+x^2-2x-1=(x^4-2x^3-x^2)+(x^2-2x-1)
    Can you proceed from here?

    --Kevin C.
    Kevin: Is there some "method" you used to factor this equation? If so, would you mind showing me ALL (and perhaps others) the steps involved? Or, do you have that rare abilitiy where you just can look at an equation like the one Christopher listed and somehow "see" its factors?

    I would appreciated it because I worked on this equation for quite a while and I could not figure out how exactly to factor it.
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  5. #5
    Super Member bigwave's Avatar
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    Cool reorder the terms

    Quote Originally Posted by ChristopherDunn View Post
    Solve: x^4-2x^3-2x-1=0
    reorder the terms

    x^4-1-2x^3-2x=0

    then

    (x^4-1)-2x(x^2+1)=0

    (x^2+1)(x^2-2x-1)=0

    x=1-\sqrt{2}
    x=1+\sqrt{2}
    Last edited by bigwave; May 4th 2010 at 01:28 PM. Reason: sign error
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