x的平方减3x加1=0,求x的三次加x三次分之一的值

题目

x的平方减3x加1=0,求x的三次加x三次分之一的值

答案

x^2-3x+1=0
x-3+1/x=0
x+1/x=3
x^3+1/x^3
=(x+1/x)(x^2-1+1/x^2)
=3(x^2-1+1/x^2)
=3(x^2+2+1/x^2-3)
=3[(x+1/x)^2-3]
=3[3^2-3]
=3*6
=18