已知x^2-5x-1=0求x^4+1/x^4的值已知x/(x^-x+1)=7求x^2/(x^4+x^2+1)的值

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已知x^2-5x-1=0求x^4+1/x^4的值已知x/(x^-x+1)=7求x^2/(x^4+x^2+1)的值
已知x^2-5x-1=0求x^4+1/x^4的值
已知x/(x^-x+1)=7求x^2/(x^4+x^2+1)的值

已知x^2-5x-1=0求x^4+1/x^4的值已知x/(x^-x+1)=7求x^2/(x^4+x^2+1)的值
x^2-5x-1=0
x-1/x=5
x^4+1/x^4=(x^2+1/x^2)^2-2={[(x-1/x)^2+2]^2-2}
={[(5)^2+2]^2-2}
=627

x^2+5x+1=0
因为x≠0
∴x+5+1/x=0
∴x+1/x=﹣5
x²+1/x²+2=25
x²+1/x²=23
x^4+2+1/﹙x^4﹚=529
x^4/﹙x^8-3x^4+1﹚
=1/[x^4-3+1/﹙x^4﹚]
=1/524
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