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已知x^2-3x+1=0,求x^3+1/x^3
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已知x^2-3x+1=0,求x^3+1/x^3
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x^2-3x+1=0
x^2+1=3x
x+1/x=3
x^3+1/x^3=(x+1/x)(x^2-1+1/x^2)=(x+1/x)[(x+1/x)²-3]=3×(3²-1)=24
x^2+1=3x
x+1/x=3
x^3+1/x^3=(x+1/x)(x^2-1+1/x^2)=(x+1/x)[(x+1/x)²-3]=3×(3²-1)=24
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