1. 若α和β為方程4x^2 - 8x - 3 = 0的根 , 試求下列各式之值:
a) 3αβ － 2α^2 － 2β^2
b) α^3 + β^3
F.4 A.MATHS
2007-10-22 5:08 am
回答 (1)
2007-10-22 5:17 am
✔ 最佳答案
a)α+β=-(-8)/4=2
αβ=-3/4
3αβ － 2α^2 － 2β^2
= -2(α^2 + β^2)+ 3αβ
= -2(α^2 + β^2 + 2αβ -2αβ)+ 3αβ
= -2(α+β)^2+4αβ+3αβ
= -2(α+β)^2+7αβ
= -2(2)^2+7(-3/4)
= -8-(21/4)
= -53/4
b)
α^3 + β^3
= (α+β)(α^2-αβ+β^2)
= (α+β)(α^2+2αβ+β^2-3αβ)
= (α+β)[(α+β)^2-3αβ]
= (2)[(2)^2-3(-3/4)]
= 2[4+(9/4)]
= 8+(9/2)
= 25/2
有錯請指正!
參考: My Maths knowledge
收錄日期: 2021-04-13 14:04:53
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20071021000051KK05126