Question

For two consecutive odd natural numbers, the square of bigger number exceeds the square of smaller number by 72. Find the two numbers.

Answer 1

Let the two consecutive even natural number be 2x + 1 and 2x + 3.
As per the given condition,
(2x + 3)² - (2x + 1)² = 72
⇒ 4x² + 12x + 9 - [4x² + 4x + 1] = 72
⇒ 4x² + 12x + 9 - 4x² - 4x - 1 = 72
⇒ 12x + 9 - 4x - 1 = 72
⇒ 8x = 64

⇒ x = `(64)/(8)`
⇒ x = 8
2x + 1 = 2(8) + 1 = 16 + 1 = 17 and 2x + 3 = 2(8) + 3 = 16 + 3 = 19
Hence, the numbers are 17 and 19.