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.

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