點解所以雙數相減都會係9既倍數?

設該雙位數是 ab，它的數值其實 = 10a + b。
所以 ab – a – b = (10a + b) – a – b = 9a – 9b = 9(a+b)
所以必定是9的倍數

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2007-09-11 10:51:16 補充：
噢！。應該是：設該雙位數是 ab，它的數值其實 = 10a + b。所以 ab – a – b = (10a + b) – a – b = 9a 所以必定是9的倍數

α is a common root of both equations implies:

α^2 + a α + b = 0 …. (1)
α^2 + b α + a = 0 …. (2)

(1) – (2) gives:

(a – b) α + b – a = 0
(a – b) α – (a – b) = 0
(a – b) (α – 1) = 0 …. (3)

Since a is not equal to b, then from (3), we know that α – 1 = 0, so α = 1.

(1) + (2) gives:
2 α^2 + a α + b α + a + b = 0
Since α =1, we have
2 + a + b + a + b = 0
=> 2 (a + b) = -2
=> (a + b) = -1