看看这道数学题

解：首先你要明白的是(x+1/x)^2=x^2+2+1/(x^2)

x^2 - x - 1 = 0
两边同时除以x(x不等于0)得
x-1-1/x=0,
x-1/x=1......(1)

(1)两边平方就得
(x-1/x)^2=1,
x^2+1/(x^2)=3.........(2)

由(2)可以变化得
x^2+2*x*1/x+1/(x^2)=3+2,
(x+1/x)^2=5
x+1/x=√5.............(3)

x^3 + 1/(x^3)
=(x+1/x)(x^2-1+1/(x^2))[公式]

将(2),(3)代入得出
(x+1/x)(x^2-1+1/(x^2))
=√5*（3-1）
=2√5