x+1/x=-3 => x^5+1/x^5=-123 的详细过程
问题描述：
x+1/x=-3 => x^5+1/x^5=-123 的详细过程
答
x^2+1/x^2=(x+1/x)^2-2=7
（x^5+1/x^5）（x+1/x）
=x^6+1/x^6+x^4+1/x^4
=(x^2+1/x^2)(x^4+1/x^4-1)+x^4+1/x^4
=(x^2+1/x^2)[(x^2+1/x^2)^2-3]+(x^2+1/x^2)^2-2
=7*(7^2-3)+7^2-2
=322+47
=369
x^5+1/x^5
=（x^5+1/x^5）（x+1/x）/(x+1/x)
=369/(-3)
=-123