Question

Find two consecutive odd positive integers, sum of whose squares is 970.

Answer 1

Let the consecutive odd positive integers be ‘a’ and a + 2 

⇒ a² + (a + 2)² = 970 

⇒ 2a² + 4a – 966 = 0 

⇒ a² + 2a – 483 = 0 

⇒ a² + 23a – 21a – 483 = 0 

⇒ a(a + 23) – 21(a + 23) = 0 

⇒ (a – 21)(a + 23) = 0 

Thus, a = 21 

Consecutive odd positive integers are 21, 23