Question

The domain of the function $f\left(x\right)=\frac{1}{\sqrt{\left(\right[x{]}^2-7\left[x\right]+10)}}$ is $(-\infty ,a)\cup [b,\infty ),$ then $a+b$ is
($\left[x\right]$ denotes the greatest integer less than or equal to $x$)

Answer 1

For $f\left(x\right)$ to be defined,
$[x{]}^2-7[x]+10>0\Rightarrow (\left[x\right]-5\left)\right(\left[x\right]-2)>0$
$\Rightarrow \left[x\right]\in (-\infty ,2)\cup (5,\infty )$
$\therefore x\in (-\infty ,2)\cup [6,\infty )$
Clearly, $a=2;b=6$
So $a+b=8$