第1个回答 2012-04-29
x^5+2x^4-5x^3+5x^2-2x-1=0
(x^5-1)+2x(x^3-1)-5x^2(x-1)=0
(x-1)(x^4+x^3+x^2+x+1+2x^3+2x^2+2x-5x^2)=0
(x-1)(x^4+3x^3-2x^2+3x+1)=0
(x-1)(x^4-x^3+x^2+4x^3-4x^2+4x+x^2-x+1)=0
(x-1)(x^2-x+1)(x^2+4x+1)=0
又x^2-x+1>0
故x-1=0或x^2+4x+1=0
解得
x=1或-2±√3本回答被提问者采纳
(x^5-1)+2x(x^3-1)-5x^2(x-1)=0
(x-1)(x^4+x^3+x^2+x+1+2x^3+2x^2+2x-5x^2)=0
(x-1)(x^4+3x^3-2x^2+3x+1)=0
(x-1)(x^4-x^3+x^2+4x^3-4x^2+4x+x^2-x+1)=0
(x-1)(x^2-x+1)(x^2+4x+1)=0
又x^2-x+1>0
故x-1=0或x^2+4x+1=0
解得
x=1或-2±√3本回答被提问者采纳
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