Let α and β be two real roots of the equation k + 1 t a n 2 x - 2 ⋅ λ tan ⁡ x = 1 - k , where k ≠ - 1 and λ are real numbers. If t a n 2 α + β = 50 , then a value of λ is

Step-by-step solution

k + 1 tan 2 ⁡ x - 2 λ tan ⁡ x + k - 1 = 0 tan ⁡ α + tan ⁡ β = 2 λ k + 1 t a n α tan ⁡ β = k - 1 k + 1 tan ⁡ α + β = 2 λ k + 1 1 - k - 1 k + 1 = 2 λ 2 = λ 2 tan 2 ⁡ α + β = λ 2 2 = 50 λ = ± 10