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Question

The set of values of $$x$$ for which the inequality $$\displaystyle \left [ x \right ]^{2}-5[x]+6\leq 0 $$ (where $$[.]$$ denote the greatest integral function) holds good are


A
2[x]<3
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B
2x<4
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C
2[x]3
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D
(b) and (c) both
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Solution

The correct option is D $$(b)$$ and $$(c)$$ both
We have,  $$\displaystyle \left [ x \right ]^{2}-5[x]+6\leq 0 $$
Let $$[x] =y$$
$$\Rightarrow y^2-5y+6\le 0$$
$$\Rightarrow (y-2)(y-3) \le 0$$
$$\Rightarrow y\in [2,3]$$
$$\Rightarrow [x]\in [2,3]$$

$$\therefore x\in [2,4)$$

Mathematics

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