Question

The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples.

Answer 1

Let the consecutive multiples of 7 be ‘a’ and a + 7 

⇒ a² + (a + 7)² = 637 

⇒ 2a² + 14a – 588 = 0 

⇒ 2a² + 42a – 28a – 588 = 0 

⇒ 2a(a + 21) – 28(a + 21) = 0 

⇒ (2a – 28)(a + 21) = 0 

Thus, a = 14 

Consecutive multiples of 7 are 14, 21