Let α ∈ 0 , π 2 and f x = x 2 + x + tan 2 ⁡ α x 2 + x , x > 0 . If the least value of f x is 2 3 , then α is equal to

Step-by-step solution

By AM-GM inequality x 2 + x + tan 2 α x 2 + x ≥ 2 ⋅ x 2 + x ⋅ tan 2 α x 2 + x = 2 tan α Since the least value of f x is 2 tan ⁡ α = 2 3 (given) Hence, α = π 3