Question

Solve for [x]² – 3[x] + 2 = 0

Answer 1

We have [x]² – 3[x] + 2 = 0

⇒ a² – 3a + 2 = 0, a = [x]

⇒ (a – 1)(a – 2) = 0

⇒ a = 1, 2 when a = 1

⇒ [x] = 1 ⇒ 1 ≤ x < 2 

⇒ x ∈ [1, 2) When a = 2

⇒ [x] = 2 ⇒ 2 ≤ x < 3

⇒ x ∈ [2, 3) Hence, the solution set is x ∈ [1, 3)