X/X^2-x+1=7 求 x^2/x^4+X^2+1的值

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X/X^2-x+1=7 求 x^2/x^4+X^2+1的值
X/X^2-x+1=7 求 x^2/x^4+X^2+1的值

X/X^2-x+1=7 求 x^2/x^4+X^2+1的值
(X/X^2-x+1)^2= x^2/x^4+X^2+1+2(X/X^2-x+1)-4
设X/X^2-x+1=Y=7 x^2/x^4+X^2+1=Z
Y^2=Z+2Y-4 因为Y=7 求得Z=39

x^4+x^2+1
= (x^2+1)^2 - x^2
= (x^2-x+1)(x^2+x+1)
x^2 / (x^4+x^2+1)
= [x^2 / (x^2-x+1)][x / (x^2+x+1)]
= 7 * [x / (x^2+x+1)]

(x^2-x+1)/x = 1/7 ,
(x^2+x+1)/x = 1...

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x^4+x^2+1
= (x^2+1)^2 - x^2
= (x^2-x+1)(x^2+x+1)
x^2 / (x^4+x^2+1)
= [x^2 / (x^2-x+1)][x / (x^2+x+1)]
= 7 * [x / (x^2+x+1)]

(x^2-x+1)/x = 1/7 ,
(x^2+x+1)/x = 1/7 + 2 = 15/7
所以: [x / (x^2+x+1)] = 7/15
因此: x^2 / (x^4+x^2+1) = 49/15
这是理论值,其实无解
因为
x/x^2-x+1=7
x=7x^2-7x+7
7x^2-8x+7=0
x^2+8/7x+1=0
x^2+1=8/7x
x+1/x=8/7
x^2+1/x^2
=(x+1/x)^2-2
=(8/7)^2-2
=64/49-2<0
因为x^2+1/x^2>0
所以x不存在
x^2/x^4+x^2+1也不存在

收起

额,这个!!!

X/X^2-x+1=7 →1/x-x=6
平方得x²+1/x²=38
x^2/x^4+X^2+1=1/x²+x²+1=39

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