x 1^2+x2^2=(x 1+x2)^2-2x 1x2=(m-2)^2-2(3m+5)=m^2-4m+4-6m- 10=m^2- 10m-6=(m-5)^2-3 1

There is no maximum value, only the minimum value is m=5: the minimum value is: -3 1.