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

http://i146.photobucket.com/albums/r...lipboard02.jpg

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 (Headbang) (Bigsmile) . 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: http://img189.imageshack.us/img189/3...3fwe525252.jpg