Question

if [x] is the integral part of x, then solve
$[4-{\left[x\right]}^2]-{\left[x\right]}^2=2$
find the number of integers satisfying the equation.

Answer 1

$[4-{\left[x\right]}^2]-{\left[x\right]}^2=2$
$\Rightarrow 4-{\left[x\right]}^2-{\left[x\right]}^2=2$
$\Rightarrow \left[x\right]=1,-1$
$\Rightarrow x\in [-1,0)\cup (1,2]$
Therefore, number of integers are 2