$PT\Leftrightarrow (\sqrt{3x^2-18x+52}-5)+(\sqrt{2x^2-12x+162}-12)+(17-\sqrt{-x^2+6x+280})=0$$\Leftrightarrow \frac{3(x-3)^2}{\sqrt{3x^2-18x+52}+5}+\frac{2(x-3)^2}{\sqrt{2x^2-12x+162}+12}+\frac{(x-3)^2}{17+\sqrt{-x^2+6x+280}}=0$
$\Leftrightarrow (x-3)^2[.......]=0$
Mà$ [.......]>0\Rightarrow (x-3)^2=0\Leftrightarrow x=3$