Question

If α, β, γ  are the roots of the equation x³ + 4x + 1 = 0, then (α + β)^–1 + (β + γ)^–1 + (α + γ)^–1 is equal to

(a) 2 

(b) 3 

(c) 4 

(d) 5

Answer 1

(c) 4

α, β, γ  are the roots of the equation x³ + 4x + 1 = 0,

∴ S₁ = α + β + γ = 0                   (Coefficient of x² = 0)

S₂ = αβ + βγ + αγ = 4

S₃ = αβγ = - 1

∴ (α + β)^–1 + (β + γ)^–1 + (α + γ)^–1