How to write f ( x ) = x n </msup> + ( 1 &#x2212;<!-- − --> x

groupweird40

groupweird40

Answered question

2022-05-28

How to write f ( x ) = x n + ( 1 x ) n in terms of r = x ( 1 x )

Answer & Explanation

Terrance Phillips

Terrance Phillips

Beginner2022-05-29Added 10 answers

More generally, the symmetric polynomial x 1 n + x 2 n can be written as a polynomial in the elementary symmetric polynomials x 1 + x 2 and x 1 x 2 :
x 1 n + x 2 n = k = 0 n / 2 a n , k ( x 1 + x 2 ) n 2 k ( x 1 x 2 ) k .
where
a n , k = ( 1 ) k n n k ( n k k ) for  k = 0 , , n / 2 .
In your case x 1 = x and x 2 = 1 x and therefore x 1 + x 2 = 1 and x 1 x 2 = x ( 1 x )

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