{"id":21986,"date":"2024-10-29T19:08:01","date_gmt":"2024-10-29T11:08:01","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/?p=21986"},"modified":"2024-12-25T00:03:07","modified_gmt":"2024-12-24T16:03:07","slug":"dse-maths-problem-solving-technique-02","status":"publish","type":"post","link":"https:\/\/www.study-together.com\/edu\/2024\/10\/dse-maths-problem-solving-technique-02\/","title":{"rendered":"DSE\u6578\u5b78\u89e3\u984c\u6280\u5de7 – \u6578\u5b78\u79d8\u6280\u5230\u5e95\u6709\u7121\u7528?"},"content":{"rendered":"\t\t
\n\t\t\t\t\t\t
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\u4eca\u65e5\u5728\u81c9\u66f8\u4e0a\u770b\u5230\u6709\u540c\u5b78\u767c\u554f\u4e00\u689d\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u7684\u984c\u76ee\u3002\u984c\u76ee\u672c\u8eab\u4e0d\u7b97\u5341\u5206\u96e3, \u4f46\u8981\u8a08\u5230\u7b54\u6848\u5176\u5be6\u6709\u4e00\u500b”\u5feb\u65b9\u6cd5”\u3002\u9019\u4ee4\u6211\u4e0d\u7981\u554f\u574a\u9593\u7684\u88dc\u7fd2\u793e\u8001\u5e2b\u4e0d\u5c11\u90fd\u6a19\u699c\u81ea\u5df1\u6709\u597d\u591a\u6578\u5b78\u79d8\u6280, \u4f46\u5230\u5e95\u9019\u4e9b\u79d8\u6280\u5230\u5e95\u5e6b\u5514\u5e6b\u5230\u624b\u5462? \u9019\u503c\u5f97\u6211\u5011\u53bb\u601d\u60f3\u4e00\u5413….<\/p>

\u8981\u505a\u9019\u689d\u984c\u76ee, \u4e00\u500b\u6bd4\u8f03\u5feb\u7684\u65b9\u6cd5\u5982\u4e0b:<\/p>

\u56e0\u70ba\u65b0\u65b9\u7a0b\u6839\u70ba 2\u03b1 – 1 \u53ca 2\u03b2 – 1, \u6545\u8a2d y = 2x – 1\u3002\u5373<\/p>

\\(x = \\dfrac{y+1}{2}\\)<\/p>

\u8981\u6c42\u7684\u65b9\u7a0b\u70ba:<\/p>

\\(\\begin{align}
a (\\dfrac{y+1}{2})^{2} + b (\\dfrac{y+1}{2}) + c &= 0 \\\\
a (y+1)^{2} + 4b(\\dfrac{y+1}{2}) + 4c &= 0 \\\\
a (y+1)^{2} + 2b(y+1) + 4c &= 0 \\\\
\\end{align}\\)<\/p>

\u7559\u610f\u4e00\u689d\u65b9\u7a0b\u7684\u8b8a\u6578\u4fc2x\u5b9a\u4fc2y\u4e26\u4e0d\u5f71\u97ff\u5230\u6839\u7684\u503c, \u6545\u7b54\u6848\u70baC\u3002<\/p>

\u4ee5\u4e0a\u7684\u65b9\u6cd5\u4e00\u822c\u8001\u5e2b\u90fd\u672a\u5fc5\u6703\u8b1b\u89e3, \u5c31\u7b97\u6709\u7528\u90fd\u672a\u5fc5\u6703\u8a73\u7d30\u89e3\u91cb\u3002\u5c0d\u6578\u5b78\u597d\u7684\u540c\u5b78\u4f86\u8aaa\u7684\u78ba\u53ef\u4ee5\u8aaa\u662f\u5b78\u5230\u4e00\u6280\u65b0\u5605\u79d8\u6280\u3002\u4f46\u5c0d\u6578\u5b78\u5514\u597d\u5605\u540c\u5b78, \u8003\u8a66\u6642\u4f62\u5730\u90fd\u597d\u53ef\u80fd\u672a\u5fc5\u60f3\u8d77\u53ef\u4ee5\u7528\u9019\u79d8\u6280\u3002<\/p>

\u4e0d\u5982\u6211\u5730\u53c8\u7747\u5413\u5982\u679c\u7528”\u50b3\u7d71”\u624b\u6cd5\u53bb\u505a, \u4f9d\u689d\u984c\u76ee\u6703\u9ede\u505a\u3002\u9996\u5148, \u56e0\u70ba\u984c\u76ee\u4fc2\u8981\u6c42\u4e00\u689d\u4ee5\u65b0\u7684\u6839\u7684\u65b9\u7a0b, \u6211\u5730\u5148\u8981\u8a08\u820a\u65b9\u7a0b\u7684 sum of roots (\u6839\u4e4b\u548c) \u53ca product of roots (\u6839\u4e4b\u7a4d)\u3002<\/p>

\u03b1 + \u03b2 = -b\/a
\u03b1\u03b2 = c\/a<\/p>

\u73fe\u8003\u616e\u65b0\u65b9\u7a0b,<\/p>

\\(\\begin{align}
sum of roots &= (2\\alpha – 1) + (2\\beta – 1) \\\\
&= 2(\\alpha + \\beta_ – 2 \\\\
&= \\dfrac{-2b}{a} – 2 \\\\<\/p>

product of roots &= (2\\alpha – 1) \\times (2\\beta – 1) \\\\
&= 4\\alpha \\beta – 2(\\alpha + \\beta) + 1 \\\\
&= \\dfrac{4c}{a} + \\dfrac{2b}{a} + 1 \\\\
&= \\dfrac{4c + 2b+ a}{a}
\\end{align}\\)<\/p>

\u6240\u4ee5\u8981\u6c42\u7684\u65b9\u7a0b\u70ba:<\/p>

\\(\\begin{align}
x^{2} +(\\dfrac{2b}{a} + 2)x + (\\dfrac{4c + 2b+ a}{a}) = 0 \\\\
ax^{2} +(2b + 2a)x + (4c + 2b+ a) = 0 \\\\
a(x^{2} + 2x + 1) + 2b(x + 1) + 4c = 0 \\\\
a(x + 1)^{2} + 2b(x + 1) + 4c = 0
\\end{align}\\)<\/p>

\u7576\u7136\uff0c\u7b54\u6848\u4e5f\u662fC\u3002<\/p>

\u53e6\u4e00\u500b\u53ef\u884c\u7684”\u5feb”\u65b9\u6cd5 (\u6578\u5b78\u79d8\u6280) \u662f<\/p>