Question

Find two consecutive numbers whose squares have the sum of 85

Answer 1

Let the consecutive numbers be ‘a’ and a + 1. 

Given, sum of squares is 85 

⇒ a² + (a+ 1)² = 85 

⇒ a² + a² + 2a + 1 = 85 

⇒ a² + a – 42 = 0 

⇒ a² + 7a – 6a – 42 = 0 

⇒ a(a + 7) – 6(a + 7) = 0 

⇒ (a – 6)(a + 7) = 0 

⇒ a = 6, -7 

Numbers are, 6, 7 or -7, -6