Question

The sum of all real roots of the equation $|x-3{|}^2+|x-3|-2=0$ is

• A. $2$
• B. $3$
• C. $4$
• D. $6$

Answer 1

Answer: (D)

$6$

Given equation is ${|x-3|}^2+|x-3|-2=0$,

To solve this equation consider $|x-3|=a$,

$a^2+a-2=0⟹(a+2)(a-1)=0$

$⟹a=-2$ or $a=1$,

But $|x-3|$ cannot be a negitive number,

$⟹|x-3|=1⟹x-3=\pm 1⟹x=4,2$,

$\therefore$ sum of all the real roots is $4+2=6$