6.9

(a) If (x1,...,xn) and (y1,...,yn), have the same elementary symmetric functions

xi = yi, i=j xiyj = i=j yiyj ,...,x1 ··· xn = y1 ··· yn, then the y’s are a permutation of the x’s.

(b) In the notation of Example 6.10, show that U is equivalent to V . [Hint: Compare the coefficients and the roots of the polynomials P(x) = O(x − ui) and Q(x) =

O(x − vi).]