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?
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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?](/uploads/image/z/8671876-52-6.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%E6%88%91%E5%8F%AA%E8%83%BD%E7%AE%97%E5%88%B0%3A%28x%5E2%2BK%2B1%2Fx%5E2%29%2F%283x%2Bk%2B3%2Fx%29%3D27+%E5%90%8E%E9%9D%A2%E6%88%91%E8%AE%BE%E7%BD%AE%E4%BA%86t%3Dx%2B1%2Fx%2Ct%5E2%3Dx%5E2%2B1%2Fx%5E2%2B2%2C%E5%B8%A6%E5%85%A5%E5%90%8E%E6%88%91%E5%B0%B1%E6%9B%B4%E5%81%9A%E4%B8%8D%E5%87%BA%E6%9D%A5%E4%BA%86%2C%E6%88%91%E6%98%AF%E5%93%AA%E9%87%8C%E5%87%BA%E7%8E%B0%E4%BA%86%E9%97%AE%E9%A2%98%3F)
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?
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?
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?
x^2+4x+1=0 .1
用1式去消减分子和分母(一个等于0的式子可以任意做加减运算),得
(14+k)x^2/(k-12)x^2=27
x不等于0,
即得(14+k)/(k-12)=27
k=13
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。