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设x/(x^2-3x+1)=1求:x^3/(x^6-27x^3+1)的值
题目详情
设x/(x^2-3x+1)=1 求:x^3/(x^6-27x^3+1)的值
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答案和解析
x/(x^2-3x+1)=1
x=x^2-3x+1
x^2+1=4x
x+1/x=4
x^2+1/x^2=(x+1/x)^2-2=16-2=14
x^3/(x^6-27x^3+1)
=1/(x^3+1/x^3-27)
=1/[(x+1/x)(x^2+1/x^2-1)-27]
=1/[4*13-27]
=1/25
x=x^2-3x+1
x^2+1=4x
x+1/x=4
x^2+1/x^2=(x+1/x)^2-2=16-2=14
x^3/(x^6-27x^3+1)
=1/(x^3+1/x^3-27)
=1/[(x+1/x)(x^2+1/x^2-1)-27]
=1/[4*13-27]
=1/25
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