Question

The difference of the squares of two consecutive even natural numbers is 68. Find the two numbers.

Answer 1

Let the two consecutive even natural numbers be 2x and 2x + 2.
As per the given condition,
(2x + 2)² - (2x)² = 68
⇒ 4x² + 8x + 4 - 4x² = 68
⇒ 8x + 4 = 68
⇒ 8x = 64

⇒ x = `(64)/(8)`
⇒ x = 8
2x = 2(8)
= 16 and 2x + 2
= 2(8) + 2
= 16 + 2
= 18
Hence, the numbers are 16 and 18.