Let a[1],a[2],...a[n] be the roots of the equation x^n -x +1=0 , where
n>=0 and a[i] ≠ 0 for all i
Evaluate ∑(r=1,n) [(a[r])^(n-1)]
[1] 表示下方的細1
Polynomials:::::
2012-06-10 8:44 pm
回答 (1)
2012-06-10 9:37 pm
✔ 最佳答案
∵xⁿ - x + 1 = 0
xⁿ = x - 1
xⁿ⁻¹ = 1 - 1/x
∴
∑ (r=1,n) arⁿ⁻¹= ∑ (r=1,n) 1 - 1/ar= n - ∑ (r=1,n) 1/ar= n - -(The coefficient of the term x / Product of roots)= n - -( -1 / 1 ) = n - 1
2012-06-10 13:55:00 補充：
n - -(The coefficient of the term x / Product of roots)
should be
n - -(The coefficient of the term x / The coefficient of the constant term)
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https://hk.answers.yahoo.com/question/index?qid=20120610000051KK00183