If [x]2 – 5 [x] + 6 = 0, where [ . ] denote the greatest integer fun

1.	If [x]2 – 5 [x] + 6 = 0, where [ . ] denote the greatest integer function, then(A) x ∈ [3, 4] (B) x ∈ (2, 3](C) x ∈ [2, 3] (D) x ∈ [2, 4)
Answer» Answer is (D) We have [x]² – 5[x] + 6 = 0 => [(x – 3)([x] – 2) = 0 => [x] = 2 , 3 . For [x] = 2, x ∈ [2, 3) For [x] = 3, x ∈ [3,4) x ∈ [2, 3) u [3,4) Or x ∈ [2,4)

If [x]2 – 5 [x] + 6 = 0, where [ . ] denote the greatest integer function, then(A) x ∈ [3, 4] (B) x ∈ (2, 3](C) x ∈ [2, 3] (D) x ∈ [2, 4)

Answer»

Answer is (D)

We have [x]² – 5[x] + 6 = 0 => [(x – 3)([x] – 2) = 0

=> [x] = 2 , 3 .

For [x] = 2, x ∈ [2, 3)

For [x] = 3, x ∈ [3,4)

x ∈ [2, 3) u [3,4)

Or x ∈ [2,4)