急! F4 sun and product of roots

17)Note that α + β = - (- 4) / 3 = 4/3 , αβ = - 5/3a)
α² + β²
= (α + β)² - 2αβ
= (4/3)² - 2(- 5/3)
= 46/9
b)
α / β + β / α
= (α² + β²) / αβ
= (46/9) / (- 5/3)
= - 46/15
c)
(α + 1/β) (β + 1/α)
= αβ + β/β + α/α + 1/αβ
= - 5/3 + 1 + 1 + - 3/5
= - 4/15
18)Note that α + β = - (-p)/1 = p , αβ = q/1 = qa)
(α + 2) (β + 2)
= αβ + 2(α + β) + 4
= q + 2p + 4
b)
α² + 3αβ + β²
= (α² + 2αβ + β²) + αβ
= (α + β)² + αβ
= p² + q
c)
1/α² + 1/β²
= (α² + β²) / (αβ)²
= ( (α + β)² - 2αβ ) / (αβ)²
= (p² - 2q) / q²
d)
(α + 2β) (β + 2α)
= αβ + 2(α² + β²) + 4αβ
= 5αβ + 2((α + β)² - 2αβ)
= 5q + 2(p² - 2q)
= 2p² + q

2011-07-27 18:22:23 補充：
Alternatively :

d)

(α + 2β) (β + 2α)
= αβ + 2(α² + β²) + 4αβ
= αβ + 2(α² + β² + 2αβ)
= αβ + 2(α + β)²
= q + 2p²

急! F4 sun and product of roots.

sun should be changed to sum .