Question

The sum of two numbers is 20, and the difference of their squares is 80. Find the numbers.

Answer 1

Here, let the two numbers be:

x and y

According to the given condition:

x + y = 20    ...(1)

x² − y² = 80    ...(2)

Using the identity:

x² − y² = (x + y)(x − y)

80 = 20(x − y)

(x − y) = `80/20`

∴ x − y = 4    ...(3)

Now, adding equations (1) and (3),

(x + y) + (x − y) = 20 + 4

x + y + x − y = 24

2x = 24

x = `24/2`

∴ x = 12

Substituting x = 12 into equation (1):

12 + y = 20

y = 20 − 12

∴ y = 8

Hence, the numbers are 12 and 8.