已知x^3-3x+1=0求x^3+1/x^3

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答案和解析

x^2-3x+1=0
乘以x得 x-3+1/x=0
∴x+1/x=3
x³+1/x³
=(x+1/x)(x²-1+1/x²)
=3×[(x²+2+1/x²)-3]
=3×[(x+1/x)²-3]
=3×(3²-3)
=18

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