Question

Solve for [x]² – 2[x] – 8 = 0

Answer 1

We have [x]² – 2[x] – 8 = 0

⇒ b² – 2b – 8 = 0, b = [x]

⇒ (b – 4)(b + 2) = 0

⇒ b = – 2, 4 when b = – 2

⇒ [x] = –2

⇒ – 2 ≤ x < 1

⇒ x ∈ [– 2, – 1) when b = 4

⇒ [x] = 4 ⇒ 4 ≤ x < 5

⇒ x ∈ [4, 5) 

Hence, the solution set is x ∈ [– 2, –1) ∪ [4, 5).