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Thread: Roots of equation

  1. #1
    Member
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    Jerusalem - Israel
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    Roots of equation

    Hi, can anyone help me to prove this:

    If the roots of the equation

    $\displaystyle x^3-Lx^2+mx+n=0$

    are the cosine of the angles of a triangle

    show that: $\displaystyle L^2=2m+2n+1$
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  2. #2
    MHF Contributor
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    Re: Roots of equation

    Well, you have three angles. Use them and see what happens.

    $\displaystyle \alpha$, $\displaystyle \beta$, $\displaystyle \pi - \alpha-\beta$

    You have a Law of Cosines.

    Show us what you get.
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