Question

The sum of two numbers is 40 and the difference of their squares is 320. Find the numbers.

Answer 1

Let the two numbers be x and y.

x + y = 40   ...(1)

x² − y² = 320

x² − y² = (x − y) (x + y)

(x − y) (x + y) = 320

Substitute x + y = 40

(x − y) ⋅ 40 = 320

x − y = 8   ...(2)

x + y = 40

From (1) and (2):

x + y = 40

x − y = 8

2x = 48

⇒ x = 24

Substitute x = 24 into x + y = 40:

y = 16

The two numbers are:

24 and 16​