一元二次方程

a)
x² + 2x - 6 = 0
Sum of roots = α + β = - 2
Product of roots = α β = - 6
α³ + β³
= (α + β) (α² - αβ + β²)
= (α + β) ( (α + β)² - 3αβ )
= (- 2) ( (- 2)² - 3(- 6) )
= - 44

b)
α , β are roots of x² + 2x - 6 = 0
∴
α² + 2α - 6 = 0 ⇒ α² = 6 - 2α
β² + 2β - 6 = 0 ⇒ β² = 6 - 2β
α³ - 5β²
= α α² - 5β²
= α (6 - 2α) - 5(6 - 2β)
= 6α - 2α² - 30 + 10β
= 6α - 2(6 - 2α) - 30 + 10β
= 10α - 12 - 30 + 10β
= 10(α + β) - 42
= 10(- 2) - 42
= - 62