已知X^2-11X+1=0,求X^2+1/X^2和X^2/(X^4+1)

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已知X^2-11X+1=0,求X^2+1/X^2和X^2/(X^4+1)已知X^2-11X+1=0,求X^2+1/X^2和X^2/(X^4+1)已知X^2-11X+1=0,求X^2+1/X^2和X^2

已知X^2-11X+1=0,求X^2+1/X^2和X^2/(X^4+1)
已知X^2-11X+1=0,求X^2+1/X^2和X^2/(X^4+1)

已知X^2-11X+1=0,求X^2+1/X^2和X^2/(X^4+1)
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X^2-11X+1=0
所以 x^2+1 =11x
两边平方:x^4+1+2x^2=121x^2
x^4+1=119x^2
所以 (x^4+1)/x^2 =119
所以X^2+1/X^2=(x^4+1)/x^2=119
X^2/(X^4+1) =1/119

已知X^2-11X+1=0,
可以得出 ,X不=0。
X^2-11X+1=0,2边都除以X得:
X-11+1/X=0
X+1/X=11
X^2+1/X^2=(X+1/X)^2-2=121-2=119
X^2/(X^4+1)的倒数是(X^4+1)/X^2=X^2+1/X^2=119
所以X^2/(X^4+1)=1/119