Let m and n be the numbers of real roots of the quadratic equations x^2-12 x+[x]+31=0 and x^2-5|x+2|-4=0 respectively, where [x] denotes the greatest…

Let m and n be the numbers of real roots of the quadratic equations $\displaystyle x^2-12 x+[x]+31=0$ and $\displaystyle x^2-5|x+2|-4=0$ respectively, where $\displaystyle [x]$ denotes the greatest integer $\displaystyle \leq x$. Then $\displaystyle \mathrm{m}^2+\mathrm{mn}+\mathrm{n}^2$ is equal to $\displaystyle \_\_\_\_$.