Question

If $[x+[x+[x+[x+\left[x\right]]]]]=10$, then $x$ lies in

• A. $[10,11)$
• B. $[2,3)$
• C. $Z$
• D. $[5,6)$

Answer 1

The correct option is B $[2,3)$

$[x+[x+[x+[x+\left[x\right]]]]]=10$
As $[x+Z]=\left[x\right]+Z$, so
$\Rightarrow [x+[x\left]\right]=\left[x\right]+\left[x\right]$
So,
$[x+[x+[x+[x+\left[x\right]]]]]=10\Rightarrow \left[x\right]+\left[x\right]+\left[x\right]+\left[x\right]+\left[x\right]=10\Rightarrow 5\left[x\right]=10\Rightarrow \left[x\right]=2\Rightarrow x=[2,3)$