急!急!急! Quadratic Equation F4

Let α and β be the roots.a)OA + OB= α + β= - (- 8) / 2= 4
b)OP = AB/2= (OB - OA)/2= (β - α) / 2= √(β - α)² / 2= √(α² + β² - 2αβ) / 2= √(α² + β² + 2αβ - 4αβ) / 2= √((α + β)² - 4αβ) / 2= √(4² - 4(3/2)) / 2= √10 / 2
20)a) α - β= √(α - β)² ..... since α - β > 0 so - √(α - β)² have rejected.= √((α² + 2αβ + β²) - 4αβ)= √((α + β)² - 4αβ)= √(- 4/2)² - 4(1/2))= √2
b)α⁴ - β⁴= (α² - β²) (α² + β²)= (α - β) (α + β) ( (α + β)² - 2αβ )= √2 (- 4/2) ( (- 4/2)² - 2(1/2) )= - 6√2

2011-07-27 21:58:05 補充：
Corrections :

b)

OP

= (OA + OB)/2

= 4/2

= 2

Thanks for remind.

OP不是2 ma?
OP = (OA+OB)/2 (Since P is the mid-pt. of A and B)
OP = (α + β)/2 = 4/2 = 2