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
解：
x^2-3x+1=0,x-3+1/x=0
(因为x不等于0，两边同时除以x)
x+1/x=3
(x+1/x)^2=9
x^2+1/x^2+2=9
x^2+1/x^2=7
x^3+1/x^3=(x+1/x)(x^2+1/x^2-1)=3*(7-1)=18
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