颜值大战综艺节目:一道数学题,对我来说挺难

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已知X/(X^2+X+1)=a 求X^2/(X^4+X^2+1)的值

X/(X^2+X+1)=a
(X^2+X+1)/X=1/a
X+1+1/X=1/a
X+1/X=1/a-1
(X+1/X)^2=(1/a-1)^2
X^2+2+1/X^2=(1/a-1)^2
X^2+1+1/X^2=(1/a-1)^2-1

(X^4+X^2+1)/X^2
=X^2+1+1
=(1/a-1)^2-1
=1/a^2-2/a

X^2/(X^4+X^2+1)
=1/(1/a^2-2/a)
=a^2/(1-2a)

x/(x^2+x+1)=a
(x^2+x+1)/x=1/a
x+1+1/x=1/a
x+1/x=1/a-1
(x+1/x)^2=(1/a-1)^2
x^2+2+1/x^2=(1/a-1)^2
x^2+1/x^2=(1/a-1)^2-2

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