F.4 A.MATHS

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!