Question

Two numbers differ by two units and the sum of their squares is 580. What are those numbers?

Answer 1

n and n+2 are the numbers and the sum of their squares is 580 so:

n^2+(n+2)^2=580

n^2+n^2+4n+4=580

2n^2+4n-576=0

2(n^2+2n-288)=0

2(n^2+18n-16n-288)=0

2(n(n+18)-16(n+18))=0

2(n-16)(n+18)=0

So there are two solutions...

16 and 18 or

-16 and -18