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))

  1. 2/5
  2. 4/5
  3. 3/5
  4. 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.