求问一道高一数学题目 求一道高一数学题。
\u95ee\u4e00\u9053\u9ad8\u4e00\u6570\u5b66\u9898\u76eehttp://www.jyeoo.com/math2/ques/detail/2390acf1-f930-4b84-9f80-d69b1aaa8ef5
\u663e\u7136loga-logb=log(a/b)
\uff081-2x2)(1+2x1)<(1+2x2)(1-2x1)
\u8fd9\u662f\u56e0\u4e3ax1<x2\u3002\u4e0a\u5f0f\u6210\u7acb\u3002
\u5219\u6709\u90a3\u4e2a\u5f0f\u5b50\uff01
\u8fd9\u4e2a\u95ee\u9898\u4e0d\u9519\uff0c\u5f88\u591a\u9ad8\u4e00\u7684\u5b66\u751f\u90fd\u5f88\u8ff7\u832b\uff0c\u5176\u5b9e\u662f\u8fd9\u6837\u7684\uff0c\u8fd9\u4e2at\u662f\u7b49\u4e8ex+1,\u4f46\u8fd9\u4e2ax\uff0c\u662f\u4e00\u76f4\u90fd\u53ea\u5c5e\u4e8ef(x+1)\u8fd9\u4e2a\u5f0f\u5b50\u7684\uff0c\u7528t\u53bb\u4ee3\u8868x,\u5c31\u662f\u7b54\u6848\u90a3\u4e2ax=t-1\uff0c\u5c06\u8fd9\u4e2a\u4ee3\u5230f(x+1)\u8fd9\u4e2a\u5f0f\u5b50\u4e2d\uff0c\u5c31\u5f97\u5230
f(t-1+1)=(t-1)^2+3(t-1)+1
\u4e8e\u662f\u5c31\u6709f(t)=t^+t-1,\u5230\u8fd9\u91cc\u4f60\u5c31\u5c06\u9898\u76ee\u7406\u89e3\u6210\u6c42f(t),\u5176\u5b9e\u7b54\u6848\u5df2\u7ecf\u51fa\u6765\u4e86\uff0c
\u5728\u8fd9\u91ccf(t)=t^+t-1\u662f\u51fd\u6570\u8868\u8fbe\u7684\u4e00\u79cd\u5f62\u5f0f\uff0c\u8fd9\u4e2at\u53ea\u662f\u8fd9\u4e2a\u51fd\u6570\u7684\u53d8\u91cf\u800c\u5df2\uff0c\u4f60\u53ef\u4ee5\u7528g,m,n\u7b49\u5176\u4ed6\u5b57\u6bcd\u8868\u793a\uff0c\u4f46\u662f\u9898\u76ee\u8bf4\u8981\u6c42f(x)\uff0c\u90a3\u53ea\u80fd\u7528x\u6765\u8868\u793a\u4e86\uff0c\u6240\u4ee5\u8981\u5c06t\u6362\u6210x\uff0c\u8fd8\u6709\u8fd9\u91cc\u7684t\u4e0d\u662f\u7b49\u4e8ex,\u9898\u76ee\u4e2d\u7684\u4e24\u4e2ax\u662f\u4e0d\u540c\u7684\uff0c\u7b2c\u4e00\u4e2ax\u662f\u53ea\u5c5e\u4e8ef(x+1)\u8fd9\u4e2a\u5f0f\u5b50\uff0c\u7b2c\u4e8c\u4e2ax\u662f\u5c5e\u4e8e\u4f60\u8981\u6c42\u7684\u90a3\u4e2a\u5f0f\u5b50\uff0ct\u4e0e\u7b2c\u4e00\u4e2ax\u6709\u5173\u7cfb\u4e3a
x+1=t \uff0ct\u8ddf\u7b2c\u4e8c\u4e2ax\u6ca1\u6709\u5173\u7cfb\uff0c\u53ea\u662f\u9898\u76ee\u8981\u4f60\u7528x\u6765\u8868\u793a\u800c\u5df2\u3002
简单计算一下即可，答案如图所示
要使“ax^2-2ax-3>0恒成立"须
1.a>0
2.4a^+12a<0
解2式得-3
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