x+1/x=-3 => x^5+1/x^5=-123 的详细过程

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/23 12:03:30
x+1/x=-3=>x^5+1/x^5=-123的详细过程x+1/x=-3=>x^5+1/x^5=-123的详细过程x+1/x=-3=>x^5+1/x^5=-123的详细过程x^2+1/x^2=(x+

x+1/x=-3 => x^5+1/x^5=-123 的详细过程
x+1/x=-3 => x^5+1/x^5=-123 的详细过程

x+1/x=-3 => x^5+1/x^5=-123 的详细过程
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