Question

If $[x{]}^2=[x+2]$, where $\left[x\right]=$ the greatest inetger less than or equal to $x$, then $x$ must be such that

• A. $x\in [1,2)$
• B. $x\in [2,3)$
• C. $x\in [-1,0)$
• D. None of these

Answer 1

Answer: (B), (C)

The correct options are
B $x\in [2,3)$
C $x\in [-1,0)$

$[x{]}^2=[x+2]\Rightarrow [x{]}^2=\left[x\right]+2$

$\Rightarrow [x{]}^2-[x]-2=0\Rightarrow (\left[x\right]+1\left)\right(\left[x\right]-2)=0$

$\Rightarrow \left[x\right]=-1,2\Rightarrow x\in [-1,0)\cup [2,3)$