Question

If $|x-7{|}^2-3|x-7|-10=0$, then value(s) of $x$ can be equal to

• A. $2$
• B. $5$
• C. $9$
• D. $12$

Answer 1

Answer: (A), (D)

$12$

$|x-7{|}^2-3|x-7|-10=0$
Let $|x-7|=t$
$\Rightarrow t^2-3t-10=0$
$\Rightarrow t^2-5t+2t-10=0$
​​​​​​​$\Rightarrow (t-5)(t+2)=0$
​​​​​​​​​​​​​​$\Rightarrow t=5\text{or}t=-2$
As $|x-7|\ge 0$, so
$\Rightarrow |x-7|=5\Rightarrow x-7=\pm 5$
$\therefore x=2,x=12$