Question

The
sum of the two positive integers multiplied by the bigger number is 204, and
their difference multiplied by the smaller number is 35. The numbers are  ?

Answer 1

let 
a,b be the integers.
and a is the bigger integer and b is the smaller integer.
as per given data,
(a+b)a=204 
=>a^2+ab=204 -(1)

and (a-b)b=35
     =>ab-b^2=35 -(2)

solving 1 and 2,we get a^2+b^2=169
                              =>so here a^2=144,b^2=25
=>a=12 and b=5
so,the numbers are 12 and 5.

Answer 2

let the numbers be a and b with a>b. therefore a(a+b)=204 and b(a-b)=35.
subtracting we get a^2+b^2=169. now we know that since a,b are positive integers a≠0 and b≠0. therefore a=12, b=5.