α和β是x²-(k-6)x+k=0的根，其中α和β都是正整數，且α>β
a.試以k代表α+β和αβ
b.証明(α-1)(β-1)=7
c.求α和β的值
中四數學(α和β)
2009-10-19 12:55 am
回答 (1)
2009-10-19 1:04 am
✔ 最佳答案
x^2 - (k-6)x + k = 0a) A + B = - [-(k-6)]/1 = k - 6
AB = k/1 = k
b)(A - 1)(B - 1)
= AB - A - B + 1
=AB - (A+B) + 1
= k - (k - 6) + 1
= 7
c)(A - 1)(B - 1) = 1 * 7
A>B , (A-1) > (B-1)
A-1 = 7
B-1 = 1
A = 8
B = 2
收錄日期: 2021-04-21 22:07:31
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https://hk.answers.yahoo.com/question/index?qid=20091018000051KK01232