若(x^2+1)/x=3，则(x^3+1/x^3+32)/(x^4+1/x^4+3)=( )。

来源：百度知道编辑：UC知道时间：2024/05/04 19:29:35

(x^2+1)/x=3
x+1/x=3

x^2+1/x^2=(x+1/x)^2-2=7
x^3+1/x^3=(x+1/x)(x^2-1+1/x^2)=3*6=18
x^4+1/x^4=(x^2+1/x^2)^2-2=47

(x^3+1/x^3+32)/(x^4+1/x^4+3)
=(18+32)/(47+3)
=50/50=1

(x^2+1)/x=3
x+(1/x)=3

(x^3+1/x^3+32)/(x^4+1/x^4+3)
={[x+(1/x)][x^2-x*(1/x)+(1/x^2)]+32}/{[x^2+(1/x^2)]^2-2*x^4*(1/x^4)+3}
=<3*{[x+(1/x)]^2-3x*(1/x)}+32>/<{[x+(1/x)]^2-2x*(1/x)}^2-2+3>
=[3*(3^2-3)+32]/[(3^2-2)^2+1]
=50/50
=1

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