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Q.
Number of solution(s) for $x$ satisfying the equation $|x-3|^{\frac{\left(x^2-8 x+15\right)}{(x-2)}}=1$, is(are)
Complex Numbers and Quadratic Equations
Solution:
$|x-3|^{\frac{\left(x^2-8 x+15\right)}{(x-2)}}=1$
$\Rightarrow x \neq 3, x \neq 2 \text { and } \frac{x^2-8 x+15}{x-2} \log |x-3|=0 $
$\Rightarrow x \neq 2, x \neq 3 \text { and }|x-3|=1 \text { or } x^2-8 x+15=0$
$\Rightarrow x \neq 2, x \neq 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 .