The sum of the squares of two consecutive odd numbers is 394. Find the numbers.

Let the consecutive odd number be ‘a’ and a + 2


a2 + (a + 2)2 = 394


2a2 + 4a – 390 = 0


a2 + 2a – 195 = 0


a2 + 15a – 13a – 195 = 0


a(a + 15) – 13(a + 15) = 0


(a – 13)(a + 15) = 0


Thus, a = 13


Consecutive odd numbers are 13, 15


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