Discussion Forum

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

Answer:

Explanation:

Let the numbers be $x$ and $y$ such that $x>y$.Then,
$x(x+y)=204 \Rightarrow x^{2}+xy = 204 ----(1)$
and $y(x-y)=35 \Rightarrow xy -y^{2}= 35 ----(2)$.
Subtracting (2) from (1), we get : $x^{2}+y^{2}=169$.
The only triplet satisfying condition is $(12,5,13)$. Thus, $x=12$, $y=5$.