Question

The difference between two numbers is 14 and the difference between their squares is 448. Find the numbers.

Answer 1

Let the larger number be x and the smaller number be y.

Then, we have:

x – y = 14 or x = 14 + y   ...(i)

x² – y² = 448   ...(ii)

On substituting x = 14 + y in (ii) we get

(14 + y)² – y² = 448

⇒ 196 + y² + 28y – y² = 448

⇒ 196 + 28y = 448

⇒ 28y = (448 – 196)

⇒ 28y = 252

⇒ `y = 252/28`

⇒ y = 9

On substituting y = 9 in (i), we get:

x = 14 + 9

x = 23

Hence, the required numbers are 23 and 9.