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Math Help - Challenging riddle

  1. #1
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    Challenging riddle

    I solved it and found it pretty challenging so I thought I could share it with you people. And please, if you already solved it beforehand or if you check on the Internet for the answer, don't ruin the fun. Thanks!

    \overline{AD} = 1cm

    \overline{EC} = 0.5 cm

    \overline{AD} = \overline{EB}

    Find \overline{DB}.

    The answer is:

    Spoiler:
    \sqrt[3]{2} or 2^{\frac{1}{3}}
    Attached Thumbnails Attached Thumbnails Challenging riddle-aaaa.jpg  
    Last edited by Sodapop; May 13th 2009 at 04:39 AM.
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  2. #2
    Moo
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    A Cute Angle Moo's Avatar
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    Hello,

    Is it AD=EB, or AD=ED ?
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  3. #3
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    Quote Originally Posted by Moo View Post
    Hello,

    Is it AD=EB, or AD=ED ?
    Wouldn't it be too easy it AD=ED? One step and you would be done ...

    It is as I stated, AD=EB.
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  4. #4
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    Thank you. I enjoyed that puzzle - not hugely taxing but very satisfying nonetheless!
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  5. #5
    Senior Member I-Think's Avatar
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    Quest.

    Hope this isn't too much of a spoiler

    How do I solve the resulting quartic equation to obtain the answer?
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  6. #6
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    Spoiler:

    Any polynomial whose coefficients are integers will, if it has an integer solution, have an integer solution that is a factor of the coefficient of the zeroth order term i.e. the constant. For example look at the general quartic:

    a x^4 + b x^3 + c x^2 + d x + e = 0

    where the coefficients a through e are integers. Well if there is an integer solution to this then it will be a factor of e. So look at that constant in your quartic and (assuming you have the right quartic) try each of it's factors to see if one is a solution. Then you can simply factor that solution out.

    Have fun!
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  7. #7
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    Quote Originally Posted by the_doc View Post
    Spoiler:

    Any polynomial whose coefficients are integers will, if it has an integer solution, have an integer solution that is a factor of the coefficient of the zeroth order term i.e. the constant. For example look at the general quartic:

    a x^4 + b x^3 + c x^2 + d x + e = 0

    where the coefficients a through e are integers. Well if there is an integer solution to this then it will be a factor of e. So look at that constant in your quartic and (assuming you have the right quartic) try each of it's factors to see if one is a solution. Then you can simply factor that solution out.

    Have fun!
    Spoiler:
    a^4 + 2a^3 - 2a - 4 = 0 becomes (a + 2)(a^3 - 2) = 0. Step by step on how to solve a quartic equation is a shotgun ammo in someone's head, trust me. xD

    I'll PM you the step by step guide though.
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