Question

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

Answer 1

Answer: 9

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