Question

the product of two number is 30 and the sum of two number is 11 what is the number

Answer 1

let the numbers be x and y 
                                      x*y = 30 
                                       y = 30/x        .................(1)
                                      x + y = 11      ..................(2)
                  substituting y = 30/x in (2)  
                             x + 30/x = 11  
                             x^2 -11x + 30
                             x^2 - 6x - 5x +30
                             x(x-6)-5(x-6)
                             (x-6)(x-5)
                              x = 6
                              x = 5
    substituting x in y = 30/x
                      if x = 6 then y = 5
               and if x = 5 then y = 6
   therefore the no. is 65 or 56               

Answer 2

let the numbers be x and y
here it's told that x*y -30
and x+y -11
so the numbers are ..
5 and 6
.. as per by trial and error method..