x-1/x=3求(x^10+x^8+x^2+1)/(x^10+x^6+x^4+1)的值

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x-1/x=3求(x^10+x^8+x^2+1)/(x^10+x^6+x^4+1)的值
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x-1/x=3求(x^10+x^8+x^2+1)/(x^10+x^6+x^4+1)的值
x-1/x=3求(x^10+x^8+x^2+1)/(x^10+x^6+x^4+1)的值

x-1/x=3求(x^10+x^8+x^2+1)/(x^10+x^6+x^4+1)的值
(x^10+x^8+x^2+1)/(x^10+x^6+x^4+1)
={(x^8+1)(x^2+1)}/{(x^4+1)(x^6+1)}
={(x^8+1)(x^2+1)}/{(x^4+1)(x^2+1)(x^4-x^2+1)}
=(x^8+1)/{(x^4+1)(x^4-x^2+1)}
=(x^4+1/x^4)/{(x^2+1/x^2)(x^2+1/x^2-1)}…………………………(1)
将分子分母同时除以x^4,得
=(x^4+1/x^4)/(x^2+1/x^2)(x^2+1/x^2-1)
由x-1/x=3,两边同时平方得,
x^2+1/x^2=11………………………………………………(2)
将上式两边同时平方得x^4+1/x^4=119……………………(3)
将(2)(3)式代入(1)式得
原式=119/110.
好难哪,费了我n个脑细胞呢.