The difference between two numbers is 14 and the difference between th

1.	The difference between two numbers is 14 and the difference between their squares is 448. Find the numbers.
Answer» 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) = 252 ⇒ y = 252/28 = 9 On substituting y = 9 in (i), we get: x = 14 + 9 = 23 Hence, the required numbers are 23 and 9.

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

Answer»

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) = 252

⇒ y = 252/28 = 9

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

x = 14 + 9 = 23

Hence, the required numbers are 23 and 9.