Question

If $S$ and $P$ are sum and product, respectively, of all real values of $x$ satisfying equation $|4-|x-1||=3$, then

• A. $S+P=4$
• B. $S-P=4$
• C. $S^2-P^2=16$
• D. All of these

Answer 1

Answer: (D)

All of these

Given $|4-|x-1||=3$

$4-|x-1|=\pm 3$

$|x-1|=1\left(or\right)7$

$x-1=\pm 1$ (or) $x-1=\pm 7$

$x=2\left(or\right)0$ (or) $x=8\left(or\right)-6$

$\therefore x=0,2,8,-6$

S=sum of all x

$=0+2-6+8=4$

P=Product of all x

$=0\times 2\times (-6)\times 8=0$

$S+P=4$ , $S-P=4$, $S^2-P^2=16$