Re: [中學] 競賽題求救
※ 引述《cheng198786 (cheng)》之銘言：
: 若a、b均為異於0之整數且二次方程式ax^2+bx+c=0之兩根恰為a、b，求a值。
: 答案為-2
: 請教教我> <
-b/a = a + b
=> b + ab + a^2 = 0
顯然a =/= -1
=> b = -a^2 / (a + 1)
且a | b => b = ak且k =/= 0
=> k = -a/(a + 1) = -1 + 1/(a + 1)
=> (k + 1)(a + 1) = 1
=> a + 1 = 1 or -1
因為a =/= 0
所以a = -2
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