Find two consecutive positive integers sum of whose square is 365

1.	Find two consecutive positive integers sum of whose square is 365
Answer» Let the two consecutive integers be x and x + 1.Then according to the question, we have:x2 + (x + 1)2 = 365⇒ x2 + x2 + 2x + 1 - 365 = 0⇒ 2x2 + 2x - 364 = 0⇒ 2(x2 + x - 182) = 0⇒x2 + x - 182 = 0⇒x2 + 14x - 13x - 182 = 0 ⇒ (x + 14) (x - 13) = 0⇒ x = -14 or x = 13Since the integers are positive, so neglecting x = -14 , we have x = 12.Hence 13, 14 are two consecutive positive integers. Thanks?? 14 and 13.

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