find two consecutive positive integers sum of whose squares is 365
Let the consecutive positive integers be x and x + 1.
Either x + 14 = 0 or x − 13 = 0, i.e., x = −14 or x = 13
Since the integers are positive, x can only be 13.
∴ x + 1 = 13 + 1 = 14
Therefore, two consecutive positive integers will be 13 and 14.