已知 X ⼀ (X2+X+1) =a,求 X2⼀（X4+X2+1）=? 。说明：X2为X平方，X4为X四次方。非常感谢

X / (X2+X+1) =a
则1/a =(x2+x+1) / x = x +1/x +1
x + 1/x = 1/a -1 两边平方
x2+ 1/x2 +2 = 1/a2 +1- 2/a
x2+1/x2 =1/a2 -2/a -1

(x4+x2+1)/ x2 =x2 +1/x2 +1 =1/a2 -2/a =(1-2a)/a2

X2/（X4+X2+1）= a2/(1-2a)

答案：a^/（1-2a）
这道题很简单啦其实。
姐姐提醒你一下哦，只需把已知条件变成倒数，待求问题也变成倒数，相信小家伙就能看出玄机啦

a＝X / (X^2+X+1) ＝1/(x+1/x+1)
∴x+1+1/x＝1/a
∴x+1/x＝1/a-1
∴(x+1/x)^2＝(1/a-1)^2＝1/a^2-2/a+1
即：x^2+2+1/x^2＝1/a^2-2/a+1
∴x^2+1+1/x^2＝1/a^2-2/a＝(1-2a)/a^2
∴1/(x^2+1+1/x^2)＝a^2/(1-2a)
∴X^2/（X^4+X2+1）＝1/(x^2+1+1/x^2)＝a^2/(1-2a)

X / (X2+X+1) =a
左边同除X
x+1/x=1/a-1
两边平方
x2+1/x2=1/a2-2/a-1
X2/（X4+X2+1）
=1/(x2+1/x2+1)
=a2/(2a2-2a+1)

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

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

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