Question

If $[x{]}^2-7[x]+10>0$, then $x$ lies in the interval
(Here, $[.]$ denotes the greatest integer function)

• A. $[6,\infty )$
• B. $(-\infty ,2)$
• C. $(-\infty ,3)$
• D. $[5,\infty )$

Answer 1

Answer: (A), (B)

The correct options are
A $[6,\infty )$
B $(-\infty ,2)$

$[x{]}^2-7[x]+10>0\Rightarrow (\left[x\right]-2\left)\right(\left[x\right]-5)>0$
$\Rightarrow -\infty <\left[x\right]<2$ or $5<\left[x\right]<\infty$
$\Rightarrow -\infty <x<2$ or $6\le x<\infty$
$\therefore x\in (-\infty ,2)\cup [6,\infty )$