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  4. Find the sum of the solution of the equation |x-3|(x2-8 x+15/x-2)=1.

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Q. Find the sum of the solution of the equation $|x-3|^{\frac{x^2-8 x+15}{x-2}}=1$.

Continuity and Differentiability

Solution:

$|x-3|^{\frac{x^2-8 x+15}{x-2}}=1$
$\frac{x^2-8 x+15}{x-2} \cdot \log |x-3|=0 $
$\frac{x^2-8 x+15}{x-2}=0 \,\,\,\, \log |x-3|=0 $
$x^2-8 x+15=0 \,\,\,\, |x-3|=1 $
$(x-3)(x-5)=0\,\,\,\, x-3= \pm 1$
$x=3, x=5\,\,\,\, x=4, x=2$
$x=3 \text { (rejected) }$
$x=2 \text { (rejected) }$
$\text { solution } x=4,5$
$\text { Sum }=4+5=9$