Question

The sum of the squares of two consecutive positive integers is 365. Find the integers.

Answer 1

Let the required two consecutive positive integers be x and (x + 1).

According to the given condition,

x² + (x + 1)² = 365

∴ x = 13  (x is a positive integers)

When x =13,

x + 1 = 13 + 1 = 14

Hence, the required positive integers are 13 and 14.