Question

If $x\in R-\left\{3\right\},$ then the possible value(s) of the expression $\frac{\sqrt{x^2-6x+9}}{3-x}+2$ can be

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (B), (D)

$3$

$\frac{\sqrt{x^2-6x+9}}{3-x}+2$
$=\frac{\sqrt{(x-3{)}^2}}{3-x}+2$
$=\frac{|x-3|}{3-x}+2$
We know that $|x-3|=\pm (x-3)$
So,
$\frac{\sqrt{x^2-6x+9}}{3-x}+2=\pm 1+2=1,3$