f.4 a.maths (10 points!!)
回答 (2)
2008-11-07 3:55 am
✔ 最佳答案
sum of roots:α+β=-bproduct of roots:αβ=c
α4 +β4=(α+β)4-4α3β-6α2β2-4αβ3
=(α+β)4-4α3β-4αβ3-6α2β2
=(α+β)4-4αβ(α2+β2)-6(αβ)2
=(α+β)4-4αβ[(α+β)2-2αβ]-6(αβ)2
=(-b)4-4c[(-b)2-2c]-6(c)2
=b4-4c(b2-2c)-6c2
=b4-4b2c+8c2-6c2
=b4-4b2c+2c2
2008-11-06 3:14 pm
1)
Sum of root : - b
Product of root : c
a^4 + p^4
= (a^2 - ap + p^2)(a^2 + ap + p^2)
= [(a + p)^2 - 3ap][(a + p)^2 - ap]
= (b^2 - 3c)(b - c)
Sum of root : - b
Product of root : c
a^4 + p^4
= (a^2 - ap + p^2)(a^2 + ap + p^2)
= [(a + p)^2 - 3ap][(a + p)^2 - ap]
= (b^2 - 3c)(b - c)
收錄日期: 2021-04-13 16:13:18
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20081105000051KK02245