Question

What are the two consecutive numbers whose squares differ by 25??

Answer 1

12 and 13

Explanation:

let the consecutive numbers be n and n + 1 , then their difference is

(n + 1)² - n² = 25 ← expand parenthesis on left side using FOIL

n² + 2n + 1 - n² = 25

2n + 1 = 25 ( subtract 1 from both sides )

2n = 24 ( divide both sides by 2 )

n = 12 and n + 1 = 12 + 1 = 13

the 2 numbers are 12 and 13 , that is

13² - 12² = 169 - 144 = 25