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Question
If [x]2 – 5[x] + 6 = 0, where [ . ] denote the greatest integer function, then ______.
Options
x ∈ [3, 4]
x ∈ (2, 3]
x ∈ [2, 3]
x ∈ [2, 4)
Solution
If [x]2 – 5[x] + 6 = 0, where [ . ] denote the greatest integer function, then x ∈ [2, 3].
Explanation:
We have [x]2 – 5[x] + 6 = 0
⇒ [x]2 – 3[x] – 2[x] + 6 = 0
⇒ [x]([x] – 3) – 2([x] – 3) = 0
⇒ ([x] – 3)([x] – 2) = 0
⇒ [x] = 2, 3
So x ∈ [2, 3].
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