若关于x的方程|x|/(x-1)=kx²有四个不等实数根，则实数k的取值范围是（负无穷，﹣4） 若关于x的方程│x│/(x-2)=kx有三个不等实数根，则k...
\u82e5\u5173\u4e8ex\u7684\u65b9\u7a0b|x|/(x-1)=kx^2\u6709\u56db\u4e2a\u4e0d\u540c\u7684\u5b9e\u6570\u6839\uff0c\u6c42k\u53d6\u503c\u8303\u56f4\u53c2\u7167\u4e0b\u9898\uff1a
\u5982\u679c\u5173\u4e8ex\u7684\u65b9\u7a0b|x|/(x+2)=kx^2\u6709\u56db\u4e2a\u4e0d\u540c\u7684\u5b9e\u6570\u6839\uff0c\u6c42\u5b9e\u6570k\u7684\u53d6\u503c\u8303\u56f4
\u8981\u6c42x\u2260-2
\u65b9\u7a0b\u5316\u4e3a|x|=kx²(x+2)
\u663e\u7136x=0\u6ee1\u8db3\u4e0a\u8ff0\u65b9\u7a0b\uff0c\u662f\u65b9\u7a0b\u7684\u4e00\u4e2a\u6839
\u82e5x\u22600
\u5219\u65b9\u7a0b\u4e24\u8fb9\u540c\u9664\u4ee5|x|\u67091=k|x|(x+2)
\u82e5x>0\uff0c\u5219\u65b9\u7a0b\u53d8\u4e3a1=kx(x+2),\u5373kx²+2kx-1=0 (1)
\u82e5x<0\uff0c\u5219\u65b9\u7a0b\u53d8\u4e3a1=-kx(x+2),\u5373kx²+2kx+1=0 (2)
\u82e5k=0\uff0c(1)(2)\u5747\u65e0\u89e3\u3002\u663e\u7136x=0\u4e0d\u662f(1)(2)\u7684\u89e3
\u82e5\u65b9\u7a0b\u6709\u56db\u4e2a\u4e0d\u540c\u7684\u5b9e\u6570\u6839\uff0c\u4e4b\u524d\u5df2\u5f97\u5230x=0\u662f\u539f\u65b9\u7a0b\u7684\u6839\uff0c\u5219\u8981\u6c42\u65b9\u7a0b(1)(2)\u67093\u4e2a\u6839
\u5bf9(1)\u82e5\u5224\u522b\u5f0f\u25b3=4k²+4k\u22650\uff0c\u5219k\u2264-1\u6216k\u22650
\u5bf9(2)\u82e5\u5224\u522b\u5f0f\u25b3=4k²-4k\u22650\uff0c\u5219k\u22640\u6216k\u22651
\u524d\u5df2\u5206\u6790k\u22600
\u82e5k\u2264-1\uff0c\u5219(1)\u6709\u4e24\u4e2a\u4e0d\u76f8\u7b49\u5b9e\u6839\uff0c\u4e24\u6839\u4e4b\u79ef\u4e3a-1/k>0\uff0c\u4e24\u6839\u4e4b\u548c\u4e3a-2,\u8bf4\u660e\u4e24\u6839\u5747\u4e3a\u8d1f\u503c\uff0c\u4f46(1)\u65b9\u7a0b\u524d\u63d0\u6761\u4ef6\u662fx>0\uff0c\u56e0\u6b64k<-1\u65f6\u65b9\u7a0b(1)\u5728x<0\u524d\u63d0\u4e0b\u65e0\u89e3\uff0c\u539f\u65b9\u7a0b\u4e0d\u53ef\u80fd\u67094\u4e2a\u4e0d\u540c\u7684\u5b9e\u6570\u6839\u3002
\u82e5-1<k<0\uff0c\uff081\uff09\u65b9\u7a0b\u65e0\u6839\uff0c\u539f\u65b9\u7a0b\u4e0d\u53ef\u80fd\u67094\u4e2a\u4e0d\u540c\u7684\u5b9e\u6570\u6839\u3002
\u82e50<k<1\uff0c\uff082\uff09\u65b9\u7a0b\u65e0\u6839\uff0c\u539f\u65b9\u7a0b\u4e0d\u53ef\u80fd\u67094\u4e2a\u4e0d\u540c\u7684\u5b9e\u6570\u6839\u3002
\u82e5k\u22651\uff0c\u65b9\u7a0b(1)\u6709\u4e24\u4e2a\u4e0d\u76f8\u7b49\u5b9e\u6839\uff0c\u4e24\u6839\u4e4b\u79ef\u4e3a-1/k0\u524d\u63d0\u4e0b\uff0c\u53ea\u6709\u4e00\u4e2a\u6b63\u6839\uff0c\u5219\u8981\u6c42(2)\u6709\u4e24\u4e2a\u4e0d\u76f8\u7b49\u7684\u8d1f\u6839\u3002\u5219k\u22601,\u8981\u6c42k>1
\u5bf9\u4e8e(2)\u6b64\u65f6\u5224\u522b\u5f0f\u25b3>0\uff0c\u4e24\u6839\u4e4b\u548c\u4e3a-2, \u4e24\u6839\u4e4b\u79ef=1/k>0\uff0c\u8bf4\u660e(2)\u6709\u4e24\u4e2a\u4e0d\u76f8\u7b49\u7684\u8d1f\u6839\uff0c\u4e4b\u524d\u8981\u6c42x\u2260-2\uff0c\u5bf9(2)\uff0c\u82e5x=-2\uff0c\u52194k-4k+1=0\uff0c\u663e\u7136x=-2\u4e0d\u662f\u65b9\u7a0b\u7684\u6839\u3002
\u7efc\u4e0a\u6240\u8ff0\uff0c\u8981\u6c42k>1
\u2502x\u2502/(x-2)=kx
kx^2-2kx=|x|
\u5f53x\u22650\u65f6\uff1a
kx^2-2kx=x
kx^2-(2k+1)x=0
x1=0
x2=2k+1\uff1e0
k\uff1e-1/2
\u5f53x\uff1c0\u65f6\uff1a
kx^2-2kx=-x
kx^2-(2k-1)x=0
x=2k-1\uff1c0
k\uff1c1/2
\u2234-1/2\uff1ck\uff1c1/2
你有点儿思维定势了，画图也一样，大概是这样
这题是要用一元二次方程做，先考虑x<0的情况，他只有一解，然后x>0必然有两解。然后利用判别式，还有正负根和系数的关系，可以得到结果
画图，k=1/|x|(x-1) 易得答案
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