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x+1/x=-3 => x^5+1/x^5=-123 的详细过程
人气:260 ℃ 时间:2020-06-26 05:51:41
解答
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
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