Discussion Forum

The difference between two positive integers is 3. If the sum of their squares is 369, then the sum of the numbers is :

Answer:

Explanation:

Let the numbers be $x$ and $(x+3)$.
Then, $x^{2}+(x+3)^{2}= 369 \Leftrightarrow x^{2}+x^{2}+9+6x = 369$
$\Leftrightarrow 2x^{2}+6x-360=0$
$\Leftrightarrow x^{2}+3x-180=0$
$\Leftrightarrow (x+15)(x-12)=0$
$\Leftrightarrow x = 12$
So, the numbers are 12 and 15
$\therefore$ Required sum = $(12+15)= 27$.