Question

The product of sum of the two numbers and sum of square of these numbers is 5500 and product of difference of the same two numbers and difference of squares of the same two numbers is 352. find these numbers.

Answer 1

(a+b)(a2+b2)= 5500
(a-b) (a2-b2) = 352 then (a-b)2(a+b) = 352 

Then: 
5500/(a2-b2) = 352/(a-b)2 


Then (a-b)2 must be a factor of 352 then (a-b)2 = 4 or (a-b)2 = 16 
But it can`t be 4, (a-b)2 = 16 
Then: a2+b2=250 (a-b) = 4 
So a solution is a = 13 and b = 9 
Answer: a = 13 and b = 9