The set of value of x for which the inequality [x]2-5[x]+6 le 0 (where [·] denote the greatest integral function) hold good if

Question

The set of value of x for which the inequality [x]2-5[x]+6 le 0 (where [·] denote the greatest integral function) hold good if (A) 2 le [x]< 3 (B) 2 le x < 4 (C) 2 le [x] le 3 (D) (b) and (c) both

Tardigrade Admin · Accepted Answer

[x]2-5 [x]+6 le 0 ⇒ ([x]-2) ([x]-3) le 0 ⇒ 2 le [x] le 3 ⇒ 2 le [x] le 3 ⇒ 2 le x le 4

Q. The set of value of x for which the inequality $[x]^{2} - 5 [x] + 6 \leq 0$ (where $[\cdot]$ denote the greatest integral function) hold good if

$2 \leq [x] < 3$

$2 \leq x < 4$

$2 \leq [x] \leq 3$

(b) and (c) both

$[x]^{2} - 5 [x] + 6 \leq 0$
$\Rightarrow ([x] - 2) ([x] - 3) \leq 0$
$\Rightarrow 2 \leq [x] \leq 3$
$\Rightarrow 2 \leq [x] \leq 3$
$\Rightarrow 2 \leq x \leq 4$

Q. The set of value of x for which the inequality [x]2−5[x]+6≤0 (where [⋅] denote the greatest integral function) hold good if

2≤[x]<3

2≤x<4

2≤[x]≤3