x^2+4x+1=0,(x^4+Kx^2+1)/(3x^3+kx^2+3x)=27,求K,
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x^2+4x+1=0,(x^4+Kx^2+1)/(3x^3+kx^2+3x)=27,求K,
我只能算到:(x^2+K+1/x^2)/(3x+k+3/x)=27 后面我设置了t=x+1/x,t^2=x^2+1/x^2+2,带入后我就更做不出来了,我是哪里出现了问题?
![](http://img.wesiedu.com/upload/4/33/433baf0de471351069acd8530c6048d5.jpg)
我只能算到:(x^2+K+1/x^2)/(3x+k+3/x)=27 后面我设置了t=x+1/x,t^2=x^2+1/x^2+2,带入后我就更做不出来了,我是哪里出现了问题?
![](http://img.wesiedu.com/upload/4/33/433baf0de471351069acd8530c6048d5.jpg)
![x^2+4x+1=0,(x^4+Kx^2+1)/(3x^3+kx^2+3x)=27,求K,](/uploads/image/z/15280786-10-6.jpg?t=x%5E2%2B4x%2B1%3D0%2C%28x%5E4%2BKx%5E2%2B1%29%2F%283x%5E3%2Bkx%5E2%2B3x%29%3D27%2C%E6%B1%82K%2C)
/>分子、分母构造x^2+4x+1
(x^4+Kx^2+1)/(3x^3+kx^2+3x)=27
[x^4+4x^3+x^2-4x^3+(k-1)x^2+1]/[3x^3+12x^2+3x+(k-12)x^2]=27
[x^2(x^2+4x+1)-4x^3-16x^2-4x+(k+15)x^2+4x+1]/[3x(x^2+4x+1)+(k-12)x^2]=27
[(k+14)x^2+x^2+4x+1]/[(k-12)x^2]=27
(k+14)/(k-12)=27
整理,得
26k=338
k=13
选D.
(x^4+Kx^2+1)/(3x^3+kx^2+3x)=27
[x^4+4x^3+x^2-4x^3+(k-1)x^2+1]/[3x^3+12x^2+3x+(k-12)x^2]=27
[x^2(x^2+4x+1)-4x^3-16x^2-4x+(k+15)x^2+4x+1]/[3x(x^2+4x+1)+(k-12)x^2]=27
[(k+14)x^2+x^2+4x+1]/[(k-12)x^2]=27
(k+14)/(k-12)=27
整理,得
26k=338
k=13
选D.
请教一道数学题:x^2+4x+1=0,(x^4+Kx^2+1)/(3x^3+kx^2+3x)=27,求K
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