Question

Find two consecutive positive integers, sum of whose squares is 365.

Answer 1

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.