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  • If [x]2 - 5[x] + 6 = 0, where [. ] denote the greatest integer function, then (a) x \in [3,4] (b) x\in (2, 3] (c) x\in [2, 3] (d) x \in [2, 4)

If[x]^2 - 5[x] + 6 = 0, where [. ] denote the greatest integer function, then
(a) x \in [3,4]
(b) x\in (2, 3]           
(c)x\in [2, 3]
(d) x \in [2, 4)

 

Answers (1)

x \in [2,3]Given data: [x]^2 - 5[x] + 6 = 0

 

Thus, [x]^2 - 3[x]2[x] + 6 = 0

[x]([x]-3) - 2([x]-3) = 0

([x]-3)([x]-2) = 0

Thus,[x] = 2,3

Or we can say that x \in [2,4)

Therefore, opt (d) is the correct option.

Posted by

infoexpert21

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