Question

The difference of two numbers is 3 and the difference of their squares is 69. Find the numbers.

Answer 1

Let one number = x

Second number = x + 3 [Difference of two numbers is 3]

According to the statement :

(x + 3)² - (x)² = 69

⇒ (x)² + (3)² + 2 × x × 3 - x² = 69 

⇒ x² + 9 + 6x - x² = 69

⇒ 6x = 69 - 9

⇒ 6x = 60

⇒ x = `60/6`

⇒ x = 10

One number = 10

Second number = x + 3 = 10 + 3 = 13