数学学习乐园讨论与解答（141―149） 标签：速算与巧算
<p><font face=" ,Arial">141</font><font face=" ,Arial">4</font><font face="宋体" lang="ZH-CN">×</font><font face=" ,Arial">4</font><font face=" ,Arial"> </font></p><p><font face=" ,Arial">34</font><font face=" ,Arial">4</font></p><p><font face="宋体" lang="ZH-CN"></font></p><p><b><font face=" ,Arial"> </font></b></p><p><b><font face=" ,Arial">142</font></b></p><p><b><font face=" ,Arial"> </font></b></p><p><font face=" ,Arial">3</font><font face="宋体" lang="ZH-CN">×</font><font face=" ,Arial">3</font><font face=" ,Arial">140</font><font face=" ,Arial">3</font><font face="宋体" lang="ZH-CN">×</font><font face=" ,Arial">3</font><font face=" ,Arial">k</font></p><p><font face=" ,Arial">A+B+C+D=a+b+c+d</font></p><p><font face=" ,Arial">A</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+B</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+C</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+D</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">=a</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+b</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+c</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+d</font><font face=" ,Arial" size="2">2</font></p><p><font face=" ,Arial">(A+k)+(B+k)+(C+k)+(D+k)</font></p><p><font face=" ,Arial">=A+B+C+D+4k</font></p><p><font face=" ,Arial">=a+b+c+d+4k</font></p><p><font face=" ,Arial">=(a+k)+(b+k)+(c+k)+(d+k)</font></p><p><font face=" ,Arial">(A+k)</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+(B+k)</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+(C+k)</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+(D+k)</font><font face=" ,Arial" size="2">2</font></p><p><font face=" ,Arial">=A</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+B</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+C</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+D</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+2k(A+B+C+D)+4k</font><font face=" ,Arial" size="2">2</font></p><p><font face=" ,Arial">=a</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+b</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+c</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+d</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+2k(a+b+c+d)+4k</font><font face=" ,Arial" size="2">2</font></p><p><font face=" ,Arial">=(a+k)</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+(b+k)</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+(c+k)</font><font face=" ,Arial" size="2">2</font><font face=" ,Arial">+(d+k)</font><font face=" ,Arial" size="2">2</font></p><p><b><font face=" ,Arial"> </font></b></p><p><b><font face=" ,Arial">143</font></b></p><p><b><font face=" ,Arial"> </font></b></p><p><font face="宋体" lang="ZH-CN"></font></p><p><font face=" ,Arial">1</font><font face=" ,Arial">2</font><font face=" ,Arial">2</font><font face=" ,Arial" size="2">11</font><font face=" ,Arial">=2023</font></p><p><b><font face=" ,Arial">11</font></b></p><p><font face=" ,Arial">11</font><font face=" ,Arial">11</font><font face=" ,Arial" size="2">4</font><font face=" ,Arial">11</font><font face=" ,Arial" size="2">5</font><font face=" ,Arial">1</font><font face=" ,Arial">5</font><font face=" ,Arial">10</font><font face=" ,Arial">10</font><font face=" ,Arial">5</font><font face=" ,Arial">1</font></p><p><font face=" ,Arial">1 4 6 4 1</font></p><p><b></b></p><p><font face=" ,Arial">a=1</font><font face=" ,Arial">2</font></p><p><font face=" ,Arial">(1+a)</font><font face=" ,Arial" size="2">-1</font><font face=" ,Arial">(1+a)</font><font face=" ,Arial" size="2">-2</font></p><p><b><font face=" ,Arial"> </font></b></p><p><b><font face=" ,Arial">145</font></b></p><p><b><font face=" ,Arial"> </font></b></p><p><font face=" ,Arial">U</font><font face=" ,Arial" size="2">n+2</font><font face=" ,Arial">=U</font><font face=" ,Arial" size="2">n+1</font><font face=" ,Arial">+U</font><font face=" ,Arial" size="2">n</font></p><p><font face=" ,Arial">1</font></p><p><font face="宋体" lang="ZH-CN"></font></p><p><font face=" ,Arial">2</font><font face=" ,Arial">AB</font><font face=" ,Arial">1</font><font face=" ,Arial">BC</font><font face=" ,Arial">A</font><font face=" ,Arial">C</font></p><p>以此类推．如果将得出的数组作向量，则其斜率就会趋近于黄金分割比．</p><p><b><font face=" ,Arial"> </font></b></p><p><b><font face=" ,Arial">146</font></b></p><p><b><font face=" ,Arial"> </font></b></p><p><font face=" ,Arial">1kg</font><font face=" ,Arial">3kg</font><font face=" ,Arial">9kg</font><font face=" ,Arial">27kg</font><font face=" ,Arial">4</font><font face=" ,Arial">1</font><font face=" ,Arial">40kg</font></p><p><font face=" ,Arial">11=9+3-1 20=27+3-9-1</font></p><p><font face=" ,Arial"><b> </b></font></p><p><b><font face=" ,Arial">147</font></b><b></b></p><p><font face=" ,Arial"><b> </b></font></p><p><b><font face=" ,Arial"> </font></b></p><p><b><font face=" ,Arial"> </font></b></p><p><b><font face=" ,Arial">149</font></b></p><p><b><font face=" ,Arial"> </font></b></p><p><font face=" ,Arial">3</font><font face=" ,Arial">9</font><font face=" ,Arial">9</font><font face=" ,Arial">9</font><font face=" ,Arial">9</font><font face=" ,Arial">3</font><font face=" ,Arial">3</font><font face=" ,Arial">3</font></p><p><font face=" ,Arial">13</font><font face=" ,Arial">12</font><font face=" ,Arial">3</font></p>
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