F.4 maths 超急 唔該幫幫手

Sum of roots = α + β = - (-2) / 1 = 2
Product of roots = α β = λ a)α² + β² = 8/3(α + β)² - 2αβ = 8/32² - 2λ = 8/3λ = 2/3
b)Since (3 + √3)/3 + (3 - √3)/3 = 2 = α + β
and (3 + √3)/3 * (3 - √3)/3 = (3² - 3)/9 = 2/3 = α β So we let α = (3 + √3)/3 , β = (3 - √3)/3 then ( (3 + √3)/3 )³ + ( (3 - √3)/3 )³= α³ + β³ = (α + β) (α² + β² - α β) = (2) (8/3 - 2/3) = 4