Please Help Me

The Sum Of Two Square Of Two Consecutive Natural Number Is 313. Find The Numbers.

1 answer

let the two numbers be n and n+1
then:
n^2 + (n+1)^2 = 313
2n^2 + 2n - 312 = 0
n^2 + n - 156 = 0
(n+13)(n-12) = 0
n = 12 or n + -13, but n> 0

the numbers are 12 and 13