若x²-3x+1=0,求分式x四次方+x²+1分之 - 知识问答

若x²-3x+1=0,求分式x四次方+x²+1分之x²的值

1个回答

x²-3x+1=0
x²=3x-1
分式x四次方+x²+1分之x²
=x^2/(x^4+x^2+1)
=x^2/(x^2(x^2+1)+1)
=x^2/((3x-1)(3x-1+1)+1)
=x^2/(9x^2-3x+1)
=x^2/(9(3x-1)-3x+1)
=x^2/(27x-9-3x+1)
=x^2/(24x-8)
=3x-1/8(3x-1)
=1/8

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