已知x+1/x=4,则(x^2)/[(x^4)+(x^2)+1]的值为多少?帮个忙!

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已知x+1/x=4,则(x^2)/[(x^4)+(x^2)+1]的值为多少?帮个忙!
已知x+1/x=4,则(x^2)/[(x^4)+(x^2)+1]的值为多少?帮个忙!

已知x+1/x=4,则(x^2)/[(x^4)+(x^2)+1]的值为多少?帮个忙!
x+1/x=4
两边平方得
x²+2+1/x²=16
x²+1/x²=14
x²/(x^4+x^2+1)
=1/(x²+1+1/x²)
=1/[(x²+1/x²)+1]
=1/(14+1)
=1/15

x+1/x=4
两边乘x
x²+1=4x
两边平方
x^4+2x²+1=16x²
两边减去x²
x^4+x²+1=15x²
所以x²/(x^4+x²+1)=1/15

[(x^4)+(x^2)+1]/(x^2)
=x^2+1+1/x^2
=(x+1/x)^2-1
=16-1
=15
(x^2)/[(x^4)+(x^2)+1]=1/15