1) Show that $x^2-m^2=8x$   As the discriminant of the polynomial is $0$

2)If $x \ge 12$  then  $x^2-10x+25 < x^2-8x < x^2$  So  $x-5 < m < x$ . As m is a positive integer so  $m=x-1$  or  $x-2$  or $x-3$  or  $x-4$. Then a little bit case work and you are done.