Question

已知x小于等于0,且x^2+1/x^2=7,求代数式(x^10+x^6+x^4+1)/(x^10+x^8+x^2+1)的值

已知x小于等于0,且x^2+1/x^2=7,求代数式(x^10+x^6+x^4+1)/(x^10+x^8+x^2+1)的值
最好有过程
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Answer 1

x^2+2+1/x^2=7+2
(x+1/x)^2=9
x<0,(x显然不等于0)
x+1/x<0
x+1/x=-3

x^3+1/x^3=(x+1/x)(x^2-1+1/x^2)=-3*(7-1)=-18

x^5+1/x^5=(x^2+1/x^2)(x^3+1/x^3)-(x+1/x)=7*(-18)-(-3)=-123

(x^10+x^6+x^4+1)/(x^10+x^8+x^2+1)
上下除x^5
=(x^5+x+1/x+1/x^5)/(x^5+x^3+1/x^3+1/x^5)
=(-123-3)/(-123-18)
=42/47