Re: [中學] 100年彰中科學班試題
※ 引述《qpzmm (欽仔)》之銘言：
: 設a、b是不為0的整數，且滿足(a－b)^2＋a(a－b)－b＝0，則數對（a，b）＝?
: (不只一組解)
用微暴力的配方法XD
(a-b)^2 +a(a-b) -b = 2a^2 -3ab +b^2 -b = 2[a-(3/4)b]^2 -(1/8)b^2 -b
= 2[a-(3/4)b]^2 -(1/8)(b+4)^2 +2 = 0
整理後得到：
16 = (b+4)^2 -(4a-3b)^2 = (4a-2b+4)(-4a+4b+4)
兩邊同除8：
2 = (2a-b+2)(-a+b+1)
因此我們可以得到：(2a-b+2,-a+b+1) = (1,2), (2,1), (-1,-2), (-2,-1)
最後可以得到：(a,b) = (-6,-8), (-6,-9)
[題外話]
看到這篇是彰中科學班的考題突然百感交加....
當年在彰中高一寫第一題競賽題時
就是看著同學用暴力配方法解二元二次方程式@@
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