Question

The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.

Answer 1

Let the two consecutive positive even numbers be x and (x + 2).

According to the given condition, 

x² + (x + 2)² = 452 

⇒ x² + x² + 4x + 4 = 452 

⇒ 2x² + 4x – 448 = 0 

⇒ x² + 2x – 224 = 0 

⇒ x² + 16x – 14x – 224 = 0 

⇒ x(x + 16) – 14(x + 16) = 0

⇒ (x + 16)(x – 14) = 0 

⇒ x + 16 = 0 or x – 14 = 0 

⇒ x = –16 or x = 14 

∴ x = 14   ...(x is a positive even number) 

When x = 14, 

x + 2 = 14 + 2

= 16 

Hence, the required numbers are 14 and 16.