Question

The difference between two positive numbers is 7 and the square of their sun is 289. Find the two numbers.

Answer 1

`x,y\in\mathbb{R}_+`

`x-y=7\\(x+y)^2=289\\\\x-y=7\\x+y=17 \vee x+y=-17`

It's not possible to get a negative number when adding two positive numbers. Therefore, we can ignore the second equation.

`x-y=7\\\underline{x+y=17}\\2x=24\\x=12\\\\12-y=7\\y=5`

The numbers are 5 and 12.