若关于x的方程x-1分之2k-x²-x分之x=x分之kx+1只有一个解，求k的值与方程的解。
\u82e5\u5173\u4e8ex\u7684\u65b9\u7a0b2k/\uff08x-1\uff09-x/\uff08x²-x\uff09=\uff08kx+1/x\u53ea\u6709\u4e00\u4e2a\u89e3\uff0c\u8bd5\u6c42k\u7684\u503c\u4e0e\u65b9\u7a0b\u7684\u89e32k/\uff08x-1\uff09-x/\uff08x²-x\uff09=\uff08kx+1)/x
\u4e24\u8fb9\u540c\u4e58\u4ee5x(x-1),\u5f97
2kx-x=(kx+1)(x-1)
2kx-x=kx²-kx+x-1
kx²-3kx+2x-1=0
\u56e0\u4e3a1\u4e2a\u89e3
\u6240\u4ee5
1.k=0
x=1/2
\u7ecf\u68c0\u9a8c\u53ef\u4ee5\u3002
2.x=1
k-3k+2-1=0
-2k=-1
k=1/2
1/2x²-3/2x+2x-1=0
x²+x-2=0
(x-1)(x+2)=0
x=1\u662f\u589e\u6839\uff0c\u53ea\u6709\u4e00\u4e2a\u6839x=-2
\u53ef\u4ee5
3. \u0394=\uff082-3k\uff09²+4k
=9k²-12k+4+4k
=9k²-8k+4=0
\u65e0\u89e3
\u6240\u4ee5
1.k=0
x=1/2
2.k=1/2
x=-2
\u7b54\uff1a
\u65b9\u7a0bkx²-(2k+1)x+k-1=0
\u5224\u522b\u5f0f\uff1a
\u25b3=[-(2k+1)]²-4k(k-1)
=8k+1
\uff081\uff09\u5f53\u6709\u4e00\u4e2a\u6839\u4e3a0\u65f6\uff0cx=0\u4ee3\u5165\u65b9\u7a0b\u5f97\uff1a
0+0+k-1=0\uff0ck=1
\uff082\uff09\u4e24\u4e2a\u6839\u4e92\u4e3a\u76f8\u53cd\u6570
\u5219\uff1a\u5224\u522b\u5f0f\u25b3=8k+1>=0\uff0ck>=-1/8\u5e76\u4e14k\u22600
\u6839\u636e\u97e6\u8fbe\u5b9a\u7406\u6709\uff1ax1+x2=(2k+1)/k=0
\u6240\u4ee5\uff1ak=-1/2
\u56e0\u6b64\uff1ak\u22600\u65f6\u4e0d\u5b58\u5728\u6ee1\u8db3\u9898\u610f\u7684k\u503c
\u6240\u4ee5\uff1ak=0\uff0cx=-1\uff0c\u4e5f\u4e0d\u6ee1\u8db3\u9898\u610f
\u7efc\u4e0a\u6240\u8ff0\uff0c\u4e0d\u5b58\u5728k\u4f7f\u5f97\u4e24\u4e2a\u5b9e\u6570\u6839\u4e92\u4e3a\u76f8\u53cd\u6570
\uff083\uff09\u6709\u4e00\u6b63\u4e00\u8d1f\u4e24\u4e2a\u6839
\u6839\u636e\u97e6\u8fbe\u5b9a\u7406\u6709\uff1a
x1*x2=(k-1)/k<0
1-1/k1\uff0c0<k<1
\u7ed3\u5408\uff082\uff09\u4e2d\u7684k>=-1/8\u4e14k\u22600\u77e5\u90530<k<1\u6ee1\u8db3\u8981\u6c42
\u6240\u4ee5\uff1a0<k<1\u65f6\u6709\u4e00\u6b63\u4e00\u8d1f\u4e24\u4e2a\u6839
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