Question 606473
let the numbers be x & y

x+y = 11
x^2+y^2= 61

x=11-y

x^2=(11-y)^2

substitute x 

(11-y)^2+y^2= 61

121-22y+y^2+y^2=61
2y^2-22y+121=61
2y^2-22y+60=0
/2
x^2-11y+30=0

x^2-6y-5y+30=0

x(x-6)-5(x-6)=0
(x-6)(x-5)=0
x= 5 OR 6

so y= 6 OR 5

(5,6) OR (6,5)