Question 250840
Let y be the smaller number , x be the larger number
 
      x-y=5 ________(1)
  x^2+y^2=233 ______(2)

from (1), x-y=5
            x=5+y___(3)

By substituting (3) into (2),

   (5+y)^2+y^2 = 233
25+10y+y^2+y^2 = 233
  2y^2+10y-208 = 0
   (y-8)(y+13) = 0  
             y = 8 or -13(rejected)   

By substituting y=8 into (3),
              x = 5 + 8
                = 13

The two positive numbers are 8 and 13