Question

The number of negative integral solutions of $x^2\cdot 2^{x+1}+2^{|x-3|+2}$ = $x^2\cdot 2^{|x-3|+4}+2^{x-1}$ is

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

Answer: (A)

The given equation can be written as
$2^{x+1}\left[x^2-\frac{1}{4}\right]=2^{|x-3|}4[4x^2-1]$
= $16\cdot 2^{|x-3|}\left[x^2-\frac{1}{4}\right]$
$\Rightarrow$ $2^{x-3}=2^{|x-3|}$
[ $\because x^2=\frac{1}{4}$ does not give negative integral value]
$\therefore$ $|x-3|=x-3$
$\therefore x\ge 3$
$\therefore$ given equation does not give any negative integral solution.