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

The correct option is D All of these

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

Either $4-|x-1|=3$ or $4-|x-1|=-3$

Taking $4-|x-1|=3$,

$|x-1|=1⟹x-1=1$ or $x-1=-1$

$\therefore x=2,x=0$

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

$|x-1|=7⟹x=8,x=-6$

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

$P=2\ast 0\ast 8\ast -6=0$

$S+P=4+0=4$

$S-P=4-0=4$

$S^2-P^2=4^2-0^2=16$