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