Q. If $\lbrack\ x\rbrack^{2} = \lbrack x + 2\rbrack,\ where\ \lbrack x\rbrack =$ the greatest integer less than or equal to $x,then\ x$ must be such that
A) $x = 2,\ - 1$
B) $\lbrack - 1,\ 0\rbrack \cup \lbrack 2,\ 3\rbrack$
C) $x \in \lbrack - 1,\ 0\rbrack$
D) None of these
Explanation
(b)
$\lbrack x\rbrack^{2} - \lbrack x\rbrack - 2 = 0$
$\Rightarrow \left( \lbrack x\rbrack - 2 \right)\left( \lbrack x\rbrack + 1 \right) = 0$
$\Rightarrow \lbrack x\rbrack = 2,\ - 1$
$\Rightarrow x \in \lbrack - 1,\ 0\rbrack \cup \lbrack 2,\ 0\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.