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Question: Answered & Verified by Expert
If $[x]$ denotes the greatest integer not exceeding $x$, then the values of $x$ satisfying $[x]^2-7[x]+12 \leq 0$ are
MathematicsFunctionsAP EAMCETAP EAMCET 2018 (23 Apr Shift 2)
Options:
  • A $1 \leq x < 4$
  • B $3 \leq x < 5$
  • C $-5 < x \leq-3$
  • D $2 \leq x \leq 4$
Solution:
1074 Upvotes Verified Answer
The correct answer is: $3 \leq x < 5$
$\begin{aligned} & \text { Given equation, } \\ & \qquad[x]^2-7[x]+12 \leq 0 \\ & \Rightarrow \quad[x]^2-4[x]-3[x]+12 \leq 0 \\ & \Rightarrow \quad([x]-4)([x]-3) \leq 0 \quad \Rightarrow \quad[x] \in[3,4] \\ & \Rightarrow \quad x \in[3,5) .\end{aligned}$

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