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x^n+x^(n-1) ………… x+1在复数域和实数域上因式分解
人气:300 ℃ 时间:2019-08-18 15:44:03
解答
在复数域上:x^n+x^(n-1) ………… x+1=(x-(cos(2π/(n+1))+isin(2π/(n+1)))(x-(cos(4π/(n+1))+isin(4π/(n+1)))……(x-(cos(2nπ/(n+1))+isin(2nπ/(n+1)))
在实数域上:当n为奇数时,x^n+x^(n-1) ………… x+1=(x+1)(x²-2cos(2π/(n+1))+1)(x²-2cos(4π/(n+1))+1)……(x²-2cos((n-1)π/(n+1))+1)
当n为偶数时,x^n+x^(n-1) ………… x+1=(x²-2cos(2π/(n+1))+1)(x²-2cos(4π/(n+1))+1)……(x²-2cos(nπ/(n+1))+1)
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