If α and β are the roots of the equation x^2 - x - 1 = 0
If α and β are the roots of the equation x2 - x - 1 = 0, then what is (α2 + β2)/((α2 - β2)(α - β))
- 2/5
- 4/5
- 3/5
- 1/5
Answer
Using the formulas of sum of roots and and product of roots, we have α + β = 1 and αβ = -1
So, α2 + β2 = (α + β)2 - 2αβ = 1 - (-2) = 3
α2 - β2 = (α + β)(α - β) = (α - β) (since (α + β) = 1)
(α - β) = √(α - β)2
(α - β)2 = α2 + β2 - 2αβ = 3 - (-2) = 5
So, (α - β) = √5
So, required expression = 3 /(√5 × √5) = 3/5
The correct option is C.