Question

Number of solution(s) for $x$ satisfying the equation $|x-3{|}^{\frac{\left(x^2-8x+15\right)}{(x-2)}}=1$, is(are)

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (A)

$|x-3{|}^{\frac{\left(x^2-8x+15\right)}{(x-2)}}=1$
$\Rightarrow x\ne 3,x\ne 2\text{ and }\frac{x^2-8x+15}{x-2}\log |x-3|=0$
$\Rightarrow x\ne 2,x\ne 3\text{ and }|x-3|=1\text{ or }{x}^2-8x+15=0$
$\Rightarrow x\ne 2,x\ne 3\text{ and }[x=2\text{ or }4\text{ or }(x-3)(x-5)=0]$
$\Rightarrow x=4\text{ or }x=5$
Therefore, the number of solutions of the given equation is 2 .