$$\begin{array}{rl}& m^2+4x=y^2+31\\ & (x^2+4x+4)-y^2=31+4\\ & (x+2{)}^2-y^2=35\\ & (x+2+y)(x+2-y)=35\end{array}$$

$\because x.y$ 为正数

$$\begin{array}{rl}& \therefore x+2+y>0,x+2+y>x+2-y\\ & \therefore \{\begin{array}{c}x+2+y=35\\ x+2-y=1\end{array}\text{ 威 }\{\begin{array}{c}x+2+y=7\\ x+2-y=5\end{array}\\ & \therefore \{\begin{array}{c}x=16\\ y=17\end{array}\text{ 或 }\{\begin{array}{c}x=4\\ y=1\end{array}\end{array}$$

$\therefore x$. y值为 16.17 成4.1.