已知x^2-3x+1=0 求x^3/x^6+3x^3+1

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已知x^2-3x+1=0求x^3/x^6+3x^3+1已知x^2-3x+1=0求x^3/x^6+3x^3+1已知x^2-3x+1=0求x^3/x^6+3x^3+1由x²-3x+1=0,可得:

已知x^2-3x+1=0 求x^3/x^6+3x^3+1
已知x^2-3x+1=0 求x^3/x^6+3x^3+1

已知x^2-3x+1=0 求x^3/x^6+3x^3+1
由 x²-3x+1=0 ,可得:
x+1/x = 3 ,
x²+1/x² = (x+1/x)²-2 = 7 ,
x³+1/x³ = (x+1/x)(x²+1/x²)-(x+1/x) = 18 ,
所以,
x^3/(x^6+1) = 1/(x³+1/x³) = 1/18 ;
x^5+1/x^5 = (x²+1/x²)(x³+1/x³)-(x+1/x) = 123 .