planet/高考数学/2021年浙江省高考数学试题.tm

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<style|<tuple|generic|chinese>>

<\body>
  <doc-data|<doc-title|2021\<#5E74\>\<#6D59\>\<#6C5F\>\<#7701\>\<#9AD8\>\<#8003\>\<#6570\>\<#5B66\>\<#8BD5\>\<#9898\>>>

  <\with|par-mode|center>
    <\section*>
      \<#7B2C\>I\<#5377\> \<#9009\>\<#62E9\>\<#9898\>\<#90E8\>\<#5206\>\<#FF08\>\<#5171\>40\<#5206\>\<#FF09\>
    </section*>
  </with>

  <subsubsection*|\<#4E00\>\<#3001\>\<#9009\>\<#62E9\>\<#9898\>>

  <\enumerate>
    <item>\<#8BBE\>\<#96C6\>\<#5408\><math|A=<around*|{|x\|x\<geqslant\>1|}>,B=<around*|{|x\|-1\<less\>x\<less\>-2|}>>\<#FF0C\>\<#5219\><math|A\<cap\>B=>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|<around*|{|x\|x\<gtr\>-1|}>>
      </cell>|<\cell>
        B. <math|<around*|{|x\|x\<geqslant\>1|}>>
      </cell>|<\cell>
        C. <math|<around*|{|x\|-1\<less\>x\<less\>1|}>>
      </cell>|<\cell>
        D. <math|<around*|{|x\|1\<leqslant\>x\<less\>2|}>>
      </cell>>>>
    </wide-tabular>

    <item>\<#5DF2\>\<#77E5\><math|a\<in\>R>\<#FF0C\><math|<around*|(|1+a i|)>
    i=3+i>\<#FF0C\>\<#FF08\><math|i>\<#4E3A\>\<#865A\>\<#6570\>\<#5355\>\<#4F4D\>\<#FF09\>\<#FF0C\>\<#5219\><math|a=>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. -1
      </cell>|<\cell>
        B. 1
      </cell>|<\cell>
        C. -3
      </cell>|<\cell>
        D. 3
      </cell>>>>
    </wide-tabular>

    <item>\<#5DF2\>\<#77E5\>\<#975E\>\<#96F6\>\<#5411\>\<#91CF\><math|<wide|a|\<vect\>>,<wide|b|\<vect\>>,<wide|c|\<vect\>>>\<#FF0C\>\<#5219\><math|<wide|a|\<vect\>>\<cdot\><wide|c|\<vect\>>=<wide|b|\<vect\>>\<cdot\><wide|c|\<vect\>>>\<#662F\><math|<wide|a|\<vect\>>=<wide|b|\<vect\>>>\<#7684\>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. \<#5145\>\<#5206\>\<#4E0D\>\<#5FC5\>\<#8981\>\<#6761\>\<#4EF6\>
      </cell>|<\cell>
        B. \<#5FC5\>\<#8981\>\<#4E0D\>\<#5145\>\<#5206\>\<#6761\>\<#4EF6\>
      </cell>>|<row|<\cell>
        C. \<#5145\>\<#5206\>\<#5FC5\>\<#8981\>\<#6761\>\<#4EF6\>
      </cell>|<\cell>
        D. \<#65E2\>\<#4E0D\>\<#5145\>\<#5206\>\<#53C8\>\<#4E0D\>\<#5FC5\>\<#8981\>\<#6761\>\<#4EF6\>
      </cell>>>>
    </wide-tabular>

    <item>\<#67D0\>\<#51E0\>\<#4F55\>\<#4F53\>\<#7684\>\<#4E09\>\<#89C6\>\<#56FE\>\<#5982\>\<#56FE\>\<#6240\>\<#793A\>\<#FF0C\>\<#5219\>\<#8BE5\>\<#51E0\>\<#4F55\>\<#4F53\>\<#7684\>\<#4F53\>\<#79EF\>\<#662F\>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|<with|math-display|true|<frac|3|2>>>
      </cell>|<\cell>
        B. 3
      </cell>|<\cell>
        C. <math|<with|math-display|true|<frac|3<sqrt|2>|2>>>
      </cell>|<\cell>
        D. <math|3<sqrt|2>>
      </cell>>>>
    </wide-tabular>

    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    <item>\<#82E5\>\<#5B9E\>\<#6570\><math|x,y>\<#6EE1\>\<#8DB3\>\<#7EA6\>\<#675F\>\<#6761\>\<#4EF6\><choice|<tformat|<table|<row|<cell|<math|x+1\<geqslant\>0>>>|<row|<cell|<math|x-y\<leqslant\>0>>>|<row|<cell|<math|2*x+3*y-1\<leqslant\>0>>>>>>\<#FF0C\>\<#5219\><math|z=x-<frac|1|2>y>\<#7684\>\<#6700\>\<#5C0F\>\<#503C\>\<#662F\>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. -2
      </cell>|<\cell>
        B. <math|-<frac|3|2>>
      </cell>|<\cell>
        C. <math|-<frac|1|2>>
      </cell>|<\cell>
        D. <math|<frac|1|10>>
      </cell>>>>
    </wide-tabular>

    <item>\<#5982\>\<#56FE\>\<#5DF2\>\<#77E5\>\<#6B63\>\<#65B9\>\<#4F53\><math|ABCD-A<rsub|1>B<rsub|1>C<rsub|1>D<rsub|1>>\<#FF0C\><math|M,N>\<#5206\>\<#522B\>\<#662F\><math|A<rsub|1>D,D<rsub|1>B>\<#7684\>\<#4E2D\>\<#70B9\>\<#FF0C\>\<#5219\>

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    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. \<#76F4\>\<#7EBF\><math|A<rsub|1>D>\<#4E0E\>\<#76F4\>\<#7EBF\><math|D<rsub|1>B>\<#5782\>\<#76F4\>\<#FF0C\>\<#76F4\>\<#7EBF\><math|MN><math|//>\<#5E73\>\<#9762\><math|ABCD>
      </cell>>|<row|<\cell>
        B. \<#76F4\>\<#7EBF\><math|A<rsub|1>D>\<#4E0E\>\<#76F4\>\<#7EBF\><math|D<rsub|1>B>\<#5E73\>\<#884C\>\<#FF0C\>\<#76F4\>\<#7EBF\><math|MN><math|\<perp\>>\<#5E73\>\<#9762\><math|BDD<rsub|1>B<rsub|1>>
      </cell>>|<row|<\cell>
        C. \<#76F4\>\<#7EBF\><math|A<rsub|1>D>\<#4E0E\>\<#76F4\>\<#7EBF\><math|D<rsub|1>B>\<#76F8\>\<#4EA4\>\<#FF0C\>\<#76F4\>\<#7EBF\><math|MN><math|//>\<#5E73\>\<#9762\><math|ABCD>
      </cell>>|<row|<\cell>
        D. \<#76F4\>\<#7EBF\><math|A<rsub|1>D>\<#4E0E\>\<#76F4\>\<#7EBF\><math|D<rsub|1>B>\<#5F02\>\<#9762\>\<#FF0C\>\<#76F4\>\<#7EBF\><math|MN><math|\<perp\>>\<#5E73\>\<#9762\><math|BDD<rsub|1>B<rsub|1>>
      </cell>>>>
    </wide-tabular>

    <item>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=x<rsup|2>+<frac|1|4>,g<around*|(|x|)>=sin
    x>\<#FF0C\>\<#5219\>\<#56FE\>\<#50CF\>\<#4E3A\>\<#5982\>\<#56FE\>\<#7684\>\<#51FD\>\<#6570\>\<#53EF\>\<#80FD\>\<#662F\>

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    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|y=f<around*|(|x|)>+g<around*|(|x|)>-<frac|1|4>>
      </cell>|<\cell>
        B. <math|y=f<around*|(|x|)>-g<around*|(|x|)>-<frac|1|4>>
      </cell>>|<row|<\cell>
        C. <math|y=f<around*|(|x|)> g<around*|(|x|)>>
      </cell>|<\cell>
        D. <math|y=<frac|g<around*|(|x|)>|f<around*|(|x|)>>>
      </cell>>>>
    </wide-tabular>

    <item>\<#5DF2\>\<#77E5\><math|\<alpha\>,\<beta\>,\<gamma\>>\<#662F\>\<#4E92\>\<#4E0D\>\<#76F8\>\<#540C\>\<#7684\>\<#9510\>\<#89D2\>\<#FF0C\>\<#5219\>\<#5728\><math|sin
    \<alpha\> cos \<beta\>,sin \<beta\> cos \<gamma\>,sin \<gamma\> cos
    \<alpha\>>\<#4E09\>\<#4E2A\>\<#503C\>\<#4E2D\>\<#FF0C\>\<#5927\>\<#4E8E\><frac|1|2>\<#7684\>\<#4E2A\>\<#6570\>\<#7684\>\<#6700\>\<#5927\>\<#503C\>\<#662F\>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. 0
      </cell>|<\cell>
        B. 1
      </cell>|<\cell>
        C. 2
      </cell>|<\cell>
        D. 3
      </cell>>>>
    </wide-tabular>

    <item>\<#5DF2\>\<#77E5\><math|a,b\<in\>R,a
    b\<gtr\>0>\<#FF0C\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=a
    x<rsup|2>+b<around*|(|x\<in\>R|)>>.\<#82E5\><math|f<around*|(|s-t|)>,f<around*|(|s|)>,f<around*|(|s+t|)>>\<#6210\>\<#7B49\>\<#6BD4\>\<#6570\>\<#5217\>\<#FF0C\>\<#5219\>\<#5E73\>\<#9762\>\<#4E0A\>\<#70B9\><math|<around*|(|s,t|)>>\<#7684\>\<#8F68\>\<#8FF9\>\<#662F\>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. \<#76F4\>\<#7EBF\>\<#548C\>\<#5706\>
      </cell>|<\cell>
        B. \<#76F4\>\<#7EBF\>\<#548C\>\<#692D\>\<#5706\>
      </cell>|<\cell>
        C. \<#76F4\>\<#7EBF\>\<#548C\>\<#53CC\>\<#66F2\>\<#7EBF\>
      </cell>|<\cell>
        D. \<#76F4\>\<#7EBF\>\<#548C\>\<#629B\>\<#7269\>\<#7EBF\>
      </cell>>>>
    </wide-tabular>

    <item>\<#5DF2\>\<#77E5\>\<#6570\>\<#5217\><math|<around*|{|a<rsub|n>|}>>\<#6EE1\>\<#8DB3\><math|a<rsub|1>=1,a<rsub|n+1>=<frac|a<rsub|n>|1+<sqrt|a<rsub|n>>><around*|(|n\<in\>N<rsup|\<ast\>><rsup|*>|)>>.\<#8BB0\>\<#6570\>\<#5217\><math|<around*|{|a<rsub|n>|}>>\<#7684\>\<#524D\><math|n>\<#9879\>\<#548C\>\<#4E3A\><math|S<rsub|n>>\<#FF0C\>\<#5219\>

    <\wide-tabular>
      <tformat|<table|<row|<\cell>
        A. <math|<frac|1|2>\<less\>S<rsub|100>\<less\><frac|3|2>>
      </cell>|<\cell>
        B. <math|3\<less\>S<rsub|100>\<less\>4>
      </cell>|<\cell>
        C. <math|4\<less\>S<rsub|100>\<less\><frac|9|2>>
      </cell>|<\cell>
        D. <math|<frac|9|2>\<less\>S<rsub|100>\<less\>5>
      </cell>>>>
    </wide-tabular>
  </enumerate>

  <\with|par-mode|center>
    <section*|\<#7B2C\>II\<#5377\> \<#975E\>\<#9009\>\<#62E9\>\<#9898\>\<#90E8\>\<#5206\>\<#FF08\>\<#5171\>110\<#5206\>\<#FF09\>>
  </with>

  <subsubsection*|\<#4E8C\>\<#3001\>\<#586B\>\<#7A7A\>\<#9898\>>

  <\enumerate>
    <assign|item-nr|10><item>\<#6211\>\<#56FD\>\<#53E4\>\<#4EE3\>\<#6570\>\<#5B66\>\<#5BB6\>\<#8D75\>\<#723D\>\<#7528\>\<#5F26\>\<#56FE\>\<#7ED9\>\<#51FA\>\<#4E86\>\<#52FE\>\<#80A1\>\<#5B9A\>\<#7406\>\<#7684\>\<#8BC1\>\<#660E\>.\<#5F26\>\<#56FE\>\<#662F\>\<#7531\>\<#56DB\>\<#4E2A\>\<#5168\>\<#7B49\>\<#7684\>\<#76F4\>\<#89D2\>\<#4E09\>\<#89D2\>\<#5F62\>\<#548C\>\<#4E2D\>\<#95F4\>\<#7684\>\<#4E00\>\<#4E2A\>\<#5C0F\>\<#6B63\>\<#65B9\>\<#5F62\>\<#62FC\>\<#6210\>\<#7684\>\<#4E00\>\<#4E2A\>\<#5927\>\<#6B63\>\<#65B9\>\<#5F62\>\<#FF08\>\<#5982\>\<#56FE\>\<#6240\>\<#793A\>\<#FF09\>.\<#82E5\>\<#76F4\>\<#89D2\>\<#4E09\>\<#89D2\>\<#5F62\>\<#76F4\>\<#89D2\>\<#8FB9\>\<#7684\>\<#957F\>\<#5206\>\<#522B\>\<#662F\>3\<#FF0C\>4\<#FF0C\>\<#8BB0\>\<#5927\>\<#6B63\>\<#65B9\>\<#5F62\>\<#7684\>\<#9762\>\<#79EF\>\<#4E3A\><math|S<rsub|1>>\<#FF0C\>\<#5C0F\>\<#6B63\>\<#65B9\>\<#5F62\>\<#7684\>\<#9762\>\<#79EF\>\<#4E3A\><math|S<rsub|2>>\<#FF0C\>\<#5219\><math|<frac|S<rsub|1>|S<rsub|2>>=><underline|<space|3em>>.

    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    <item>\<#5DF2\>\<#77E5\><math|a\<in\>R>\<#FF0C\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=><choice|<tformat|<table|<row|<cell|<math|x<rsup|2>-4>,>|<cell|<math|x\<gtr\>2>>>|<row|<cell|<math|<around*|\||x-3|\|>+a>,>|<cell|<math|x\<leqslant\>2>>>>>>\<#FF0C\>\<#82E5\><math|f<around*|[|f<around*|(|<sqrt|6>|)>|]>=3>\<#FF0C\>\<#5219\><math|a=><underline|<space|3em>>.

    <item>\<#5DF2\>\<#77E5\>\<#591A\>\<#9879\>\<#5F0F\><math|<around*|(|x-1|)><rsup|3>+<around*|(|x+1|)><rsup|4>=x<rsup|4>+a<rsub|1>*x<rsup|3>+a<rsub|2>x<rsup|2>+a<rsub|3>*x+a<rsub|4>>\<#FF0C\>\<#5219\><math|a<rsub|1>=><underline|<space|3em>>\<#FF0C\><math|a<rsub|2>+a<rsub|3>+a<rsub|4>=><underline|<space|3em>>.

    <item>\<#5728\><math|\<triangle\>ABC>\<#4E2D\>\<#FF0C\><math|\<angle\>B=60<rsup|\<circ\>><rsup|>>\<#FF0C\><math|AB=2>\<#FF0C\><math|M>\<#662F\><math|BC>\<#7684\>\<#4E2D\>\<#70B9\>\<#FF0C\><math|AM=2<sqrt|3>>\<#FF0C\>\<#5219\><math|AC=><underline|<space|3em>>\<#FF0C\><math|cos\<angle\>MAC=><underline|<space|3em>>.

    <item>\<#888B\>\<#4E2D\>\<#6709\>4\<#4E2A\>\<#7EA2\>\<#7403\><math|m>\<#4E2A\>\<#9EC4\>\<#7403\>\<#FF0C\><math|n>\<#4E2A\>\<#7EFF\>\<#7403\>.
    \<#73B0\>\<#4ECE\>\<#4E2D\>\<#4EFB\>\<#53D6\>\<#4E24\>\<#4E2A\>\<#7403\>\<#FF0C\>\<#8BB0\>\<#53D6\>\<#51FA\>\<#7684\>\<#7EA2\>\<#7403\>\<#6570\>\<#4E3A\><math|\<xi\>>\<#FF0C\>\<#82E5\>\<#53D6\>\<#51FA\>\<#7684\>\<#4E24\>\<#4E2A\>\<#7403\>\<#90FD\>\<#662F\>\<#7EA2\>\<#7403\>\<#7684\>\<#6982\>\<#7387\>\<#4E3A\><frac|1|6>\<#FF0C\>\<#4E00\>\<#7EA2\>\<#4E00\>\<#9EC4\>\<#7684\>\<#6982\>\<#7387\>\<#4E3A\><frac|1|3>\<#FF0C\>\<#5219\><math|m-n=><underline|<space|3em>>\<#FF0C\><math|E<around*|(|\<xi\>|)>=><underline|<space|3em>>.

    <item>\<#5DF2\>\<#77E5\>\<#692D\>\<#5706\><math|<frac|x<rsup|2>|a<rsup|2>>+<frac|y<rsup|2>|b<rsup|2>>=1<around*|(|a\<gtr\>b\<gtr\>0|)>>\<#FF0C\>\<#7126\>\<#70B9\><math|F<rsub|1><around*|(|-c,0|)>>\<#FF0C\><math|F<rsub|2><around*|(|c,0|)><around*|(|c\<gtr\>0|)>>\<#FF0C\>\<#82E5\>\<#8FC7\><math|F<rsub|1>>\<#7684\>\<#76F4\>\<#7EBF\>\<#548C\>\<#5706\><math|<around*|(|x-<frac|1|2>c|)><rsup|2>+y<rsup|2>=c<rsup|2>>\<#76F8\>\<#5207\>\<#FF0C\>\<#4E0E\>\<#692D\>\<#5706\>\<#5728\>\<#7B2C\>\<#4E00\>\<#8C61\>\<#9650\>\<#4EA4\>\<#4E8E\>\<#70B9\><math|P>\<#FF0C\>\<#4E14\><math|PF<rsub|2>\<perp\>x>\<#8F74\>\<#FF0C\>\<#5219\>\<#8BE5\>\<#76F4\>\<#7EBF\>\<#7684\>\<#659C\>\<#7387\>\<#662F\><underline|<space|3em>>\<#FF0C\>\<#692D\>\<#5706\>\<#7684\>\<#79BB\>\<#5FC3\>\<#7387\>\<#662F\><underline|<space|3em>>.

    <item>\<#5DF2\>\<#77E5\>\<#5E73\>\<#9762\>\<#5411\>\<#91CF\><math|<wide|a|\<vect\>>,<wide|b|\<vect\>>,<wide|c|\<vect\>>,<around*|(|<wide|c|\<vect\>>\<neq\>0|)>>\<#6EE1\>\<#8DB3\><math|<around*|\||<wide|a|\<vect\>>|\|>=1,<around*|\||<wide|b|\<vect\>>|\|>=2,<around*|(|<wide|a|\<vect\>>-<wide|b|\<vect\>>|)>\<cdot\><wide|c|\<vect\>>=0>.
    \<#8BB0\>\<#5411\>\<#91CF\><math|<wide|d|\<vect\>>>\<#5728\><math|<wide|a|\<vect\>>,<wide|b|\<vect\>>>\<#65B9\>\<#5411\>\<#4E0A\>\<#7684\>\<#6295\>\<#5F71\>\<#5206\>\<#522B\>\<#4E3A\><math|x>\<#FF0C\><math|y>\<#FF0C\><math|<wide|d|\<vect\>>-<wide|a|\<vect\>>>\<#5728\><math|<wide|c|\<vect\>>>\<#65B9\>\<#5411\>\<#4E0A\>\<#7684\>\<#6295\>\<#5F71\>\<#4E3A\><math|z>\<#FF0C\>\<#5219\><math|x<rsup|2>+y<rsup|2>+z<rsup|2>>\<#7684\>\<#6700\>\<#5C0F\>\<#503C\>\<#4E3A\><underline|<space|3em>>.
  </enumerate>

  <subsubsection*|\<#4E09\>\<#3001\>\<#89E3\>\<#7B54\>\<#9898\>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>5\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>74\<#5206\>\<#FF0C\>\<#89E3\>\<#7B54\>\<#5E94\>\<#5199\>\<#51FA\>\<#6587\>\<#5B57\>\<#8BF4\>\<#660E\>\<#3001\>\<#8BC1\>\<#660E\>\<#8FC7\>\<#7A0B\>\<#6216\>\<#6F14\>\<#7B97\>\<#6B65\>\<#9AA4\>\<#3002\>\<#FF09\>>

  <\enumerate>
    <assign|item-nr|17><item>\<#8BBE\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=sin
    x+cos x <around*|(|x\<in\>R|)>>.

    <\enumerate-alpha>
      <item>\<#6C42\>\<#51FD\>\<#6570\><math|y=<around*|[|f<around*|(|x+<frac|\<pi\>|2>|)>|]><rsup|2>>\<#7684\>\<#6700\>\<#5C0F\>\<#6B63\>\<#5468\>\<#671F\>\<#FF1B\>

      <item>\<#6C42\>\<#51FD\>\<#6570\><math|y=f<around*|(|x|)>f<around*|(|x-<frac|\<pi\>|2>|)>>\<#5728\><math|<around*|[|0,<frac|\<pi\>|2>|]>>\<#4E0A\>\<#7684\>\<#6700\>\<#5927\>\<#503C\>.
    </enumerate-alpha>

    <item>\<#5982\>\<#56FE\>\<#FF0C\>\<#5728\>\<#56DB\>\<#68F1\>\<#9525\><math|P-ABCD>\<#4E2D\>\<#FF0C\>\<#5E95\>\<#9762\><math|ABCD>\<#662F\>\<#5E73\>\<#884C\>\<#56DB\>\<#8FB9\>\<#5F62\>\<#FF0C\><math|\<angle\>ABC=120<rsup|\<circ\>>>\<#FF0C\><math|AB=1>\<#FF0C\><math|BC=4>\<#FF0C\><math|PA=<sqrt|15>>\<#FF0C\><math|M,N>\<#5206\>\<#522B\>\<#4E3A\><math|BC,PC>\<#7684\>\<#4E2D\>\<#70B9\>\<#FF0C\><math|PD\<bot\>DC>\<#FF0C\><math|PM\<bot\>MD>.

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    <\enumerate-alpha>
      <item>\<#6C42\>\<#629B\>\<#7269\>\<#7EBF\>\<#7684\>\<#65B9\>\<#7A0B\>\<#FF1B\>

      <item>\<#8BBE\>\<#8FC7\>\<#70B9\>F\<#7684\>\<#76F4\>\<#7EBF\>\<#4EA4\>\<#629B\>\<#7269\>\<#7EBF\>\<#4E0E\>A\<#3001\>B\<#4E24\>\<#70B9\>\<#FF0C\>\<#659C\>\<#7387\>\<#4E3A\>2\<#7684\>\<#76F4\>\<#7EBF\><math|l>\<#4E0E\>\<#76F4\>\<#7EBF\><math|MA>\<#FF0C\><math|MB>\<#FF0C\><math|AB>\<#FF0C\><math|x>\<#8F74\>\<#4F9D\>\<#6B21\>\<#4EA4\>\<#4E8E\>\<#70B9\>P\<#FF0C\>Q\<#FF0C\>R\<#FF0C\>N\<#FF0C\>\<#4E14\><math|<around*|\||RN|\|><rsup|2>=<around*|\||PN|\|>\<cdot\><around*|\||QN|\|>>\<#FF0C\>\<#6C42\>\<#76F4\>\<#7EBF\><math|l>\<#5728\><math|x>\<#8F74\>\<#4E0A\>\<#622A\>\<#8DDD\>\<#7684\>\<#8303\>\<#56F4\>.
    </enumerate-alpha>

    <item>\<#8BBE\><math|a>\<#FF0C\><math|b>\<#4E3A\>\<#5B9E\>\<#6570\>\<#FF0C\>\<#4E14\><math|a\<gtr\>1>\<#FF0C\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>=a<rsup|x>-b
    x+e<rsup|2><around*|(|x\<in\>R|)>>

    <\enumerate-alpha>
      <item>\<#6C42\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>>\<#7684\>\<#5355\>\<#8C03\>\<#533A\>\<#95F4\>\<#FF1B\>

      <item>\<#82E5\>\<#5BF9\>\<#4EFB\>\<#610F\><math|b\<gtr\>2e<rsup|2>>\<#FF0C\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>>\<#6709\>\<#4E24\>\<#4E2A\>\<#4E0D\>\<#540C\>\<#7684\>\<#96F6\>\<#70B9\>\<#FF0C\>\<#6C42\><math|a>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>\<#FF1B\>

      <item>\<#5F53\><math|a=e>\<#65F6\>\<#FF0C\>\<#8BC1\>\<#660E\>\<#FF1A\>\<#5BF9\>\<#4EFB\>\<#610F\><math|b\<gtr\>e<rsup|4>>\<#FF0C\>\<#51FD\>\<#6570\><math|f<around*|(|x|)>>\<#6709\>\<#4E24\>\<#4E2A\>\<#4E0D\>\<#540C\>\<#7684\>\<#96F6\>\<#70B9\><math|x<rsub|1>>\<#FF0C\><math|x<rsub|2>>\<#FF0C\>\<#6EE1\>\<#8DB3\><math|x<rsub|2>\<gtr\><frac|b
      ln b|2 e<rsup|2>>x<rsub|1>+<frac|e<rsup|2>|b>>.
    </enumerate-alpha>

    \<#FF08\>\<#6CE8\>\<#FF1A\><math|e=2.71828\<ldots\>>\<#662F\>\<#81EA\>\<#7136\>\<#5BF9\>\<#6570\>\<#7684\>\<#5E95\>\<#6570\>\<#FF09\>
  </enumerate>

  <\note*>
    \<#672C\>\<#8BD5\>\<#5377\>\<#4F7F\>\<#7528\><hlink|\<#58A8\>\<#5E72\>\<#7F16\>\<#8F91\>\<#5668\>|https://gitee.com/XmacsLabs/mogan/>\<#5236\>\<#4F5C\>\<#3002\>
  </note*>
</body>

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      <with|par-left|<quote|2tab>|\<#4E09\>\<#3001\>\<#89E3\>\<#7B54\>\<#9898\>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>5\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>74\<#5206\>\<#FF0C\>\<#89E3\>\<#7B54\>\<#5E94\>\<#5199\>\<#51FA\>\<#6587\>\<#5B57\>\<#8BF4\>\<#660E\>\<#3001\>\<#8BC1\>\<#660E\>\<#8FC7\>\<#7A0B\>\<#6216\>\<#6F14\>\<#7B97\>\<#6B65\>\<#9AA4\>\<#3002\>\<#FF09\>
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