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Thread: Thinking problem [Newton's Polynomial]

  1. #1
    Junior Member
    Jun 2010

    Thinking problem [Newton's Polynomial]

    I hope this is the right section where i should post this.

    The translation:

    Let a, b, c be the coeff. of a 2nd degree equation $\displaystyle ax^2+bx+c=0$ with x and y as roots (real numbers or complex). For any n (natural number), without solving the equation determine $\displaystyle S_n=x^n+y^n$. "par" means even, "impar" means odd

    I used newton's polynomial to expand $\displaystyle (x+y)^n$ and it gave me that sum or whatever. For n = 2 and n = 3 i got the result from Viete's formulas. For n > 3 it's a long story . I had to brake it into two...for even number and odd numbers, otherwise i couldn't find a general form for Sn.

    I still got the paper where i solved using newton for n = 4, 5, 6, 7 ... and from there i could deduce a general formula.

    I want to know one thing: Is it correct?

    I hope you "understand" my question...

    Damn... picture too big for LATEX... here it is:
    Last edited by Utherr; Jun 26th 2010 at 01:04 PM.
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