\u4e00\u9053\u9ad8\u4e00\u6570\u5b66\u9898(\u6025)

\u4ed4\u7ec6\u770b\u4e24\u4e2a\u96c6\u5408\u7684\u8868\u793a\u65b9\u6cd5
\u96c6\u5408{x|ax²+2x+1=0}\u7528\u7684\u662f\u63cf\u8ff0\u6cd5\uff0c\u96c6\u5408\u63cf\u8ff0\u5bf9\u8c61\u662fx\uff0c\u96c6\u5408\u7684\u5143\u7d20\u662f\u5173\u4e8ex\u7684\u65b9\u7a0bax²+2x+1=0\u7684\u89e3
\u800c\u96c6\u5408{x²-1=0}\u7528\u7684\u662f\u5217\u4e3e\u6cd5\uff0c\u96c6\u5408\u7684\u5143\u7d20\u5c31\u662f\u65b9\u7a0bx²-1=0

\u6240\u4ee5\u96c6\u5408{x²-1=0}\u7684\u5143\u7d20\u662f1\u4e2a\uff0c\u7531\u4e8e\u4e24\u4e2a\u96c6\u5408\u7684\u5143\u7d20\u4e2a\u6570\u76f8\u540c\uff0c\u6240\u4ee5\u96c6\u5408{x|ax²+2x+1=0}\u4e5f\u662f\u67091\u4e2a\u5143\u7d20\uff0c\u5373\u662f\u5173\u4e8ex\u7684\u65b9\u7a0bax²+2x+1=0\u6709\u4e14\u53ea\u67091\u4e2a\u6839
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\u2460\u65b9\u7a0bax²+2x+1=0\u662f\u4e00\u6b21\u65b9\u7a0b\uff0c\u5373\u4e8c\u6b21\u9879\u7cfb\u6570\u4e3a0\uff0c\u6b64\u65f6a=0
\u2461\u4ee3\u6570\u5f0fax²+2x+1\u6784\u6210\u5b8c\u5168\u5e73\u65b9\u5f0f\uff0c\u5373ax²+2x+1=a(x+1/a)²+1-1/a\uff0c\u5176\u4e2da(x+1/a)²\u662f\u5b8c\u5168\u5e73\u65b9\u5f0f\uff0c\u6240\u4ee51-1/a=0\uff0c\u89e3\u5f97a=1
\u7efc\u5408\u5f97a\u7684\u53d6\u503c\u96c6\u5408\u4e3a{0,1}

\u7b49\u8170\u68af\u5f62\u7684\u4e0b\u5e95\u662fb\uff0c
\u4e0a\u5e95\u662fb+2*a*cos60\u00b0=b+a
\u9ad8\u662f a*sin60\u00b0=a \u6839\u53f73/2
\u56e0\u6b64\u68af\u5f62\u7684\u9762\u79ef\u662f
S=(1/2)*\uff08b+b+a\uff09*a \u6839\u53f73/2
=(2b+a)*a \u6839\u53f73/4
\u53ef\u5f97b=\uff084S/a\u6839\u53f73-a\uff09/2
\u6240\u4ee5\u7528\u6599Y\u4e3a\uff1a Y=b+2a= 2S/a\u6839\u53f73+3a/2=2S/\u6839\u53f73*a-1+3a/2 \u5176\u4e2dS\u4e3a\u5e38\u6570
\u56e0\u6b64Y'=-2S/\u6839\u53f73a+3/2
\u56e0\u6b64\u5f53Y'=0\uff0c\u5373 a= 3\u6839\u53f73/4S \u65f6\uff0cY\u6709\u6700\u5c0f\u503c
\u6b64\u65f6b=8S^2/9-3\u6839\u53f73/8S
\u56e0\u6b64a:b= 3\u6839\u53f73/4S \uff1a\uff088S^2/9-3\u6839\u53f73/8S\uff09