solve the equation x^5-5x^4+9x^3-9x^2+5x-1=0
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The above equation can be re-arranged as
(x^5-1)+9x^2(x-1)+5x(1-x^3)=0
(x-1)(x^4+x^3+x^2+x+1)+9x^2(x-1)-5x(x-1)(x^2+x+1)=0
(x-1)(x^4+x^3+x^2+x+1+9x^2-5x^3-5x^2-5x)=0
(x-1)(x^4-4x^3+5x^2-4x+1)=0
Hence x=1 is a solution
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