已知x²-3x+1=0,求x³+1/(x³)的值

已知x²-3x+1=0,求x³+1/(x³)的值
已知x²-3x+1=0,求x³+1/(x³)的值

已知x²-3x+1=0,求x³+1/(x³)的值
题 目
(x^3+1)/x^3?还是x^3 + 1/x^3?
应该是后面的吧
x²-3x+1=0 ,得x^2=3x-1,
所以 x^3=x(3x-1)=3x^2-x=3(3x-1)-x=8x-3
x^3 + 1/x^3=(8x-3)+1/(8x-3)
=[(8x-3)^2+1]/(8x-3)
=(64x^2-48x+10)/(8x-3)
=(192x-64-48x+10)/(8x-3)
=(144x-54)/(8x-3)
=18

x²-3x+1=0
x-3+1/x=0
x+1/x=3
x²+1/x²
=(x+1/x)²-2
=3²-2
=7
x³+1/x³
=(x+1/x)(x²-1+1/x²)
=3*(7-1)
=3*6
=18

解
x²-3x+1=0
x+1/x=3
x³+1/(x³)
=(x+1/x)(x^2-x*1/x+1/x^2)
=(x+1/x)[(x+1/x)^2-3x*1/x]
=(x+1/x)[(x+1/x)^2-3]
=3(3^2-3)
=18