Question

One positive integer is 5 less than twice another. The sum of their squares is 610. How do you find the integers?

Answer 1

`x=21, y=13`

Explanation:

`x^2+y^2=610`

`x=2y-5`

Substitute `x=2y-5` into `x^2+y^2=610`

`(2y-5)^2+y^2=610`

`4y^2-20y+25+y^2=610`

`5y^2-20y-585=0`

Divide by 5

`y^2-4y-117=0`

`(y+9)(y-13)=0`

`y=-9 or y=13`

If `y=-9, x=2xx-9-5=-23`

if `y=13, x=2xx13-5=21`

Has to be the positive integers