Question

The difference between two numbers is 14 and the difference between their squares is 448, then find the numbers.

Answer 1

23, 9

Explanation:

Let a, b - be the numbers.

`a-b = 14\\a^2-b^2=448 = (a-b)(a+b) = 448\\(14)(a+b)=448\\a+ b = 448/14 = 32`

`a - b = 14\\a + b = 32\\2a = 46\\a = 23 => b = 9`

Answer 2

Answer with Step-by-step explanation:

Let a, b be the two numbers.

The difference between two numbers is 14

i.e. a-b=14 -------(1)

The difference between their squares is 448

i.e.

`a^2-b^2=448`

i.e. (a-b)(a+b) = 448

(14)(a+b)=448

a+ b = 448/14

a+b = 32 --------(2)

Adding equation (1) and (2)

a-b+a+b=14+32

2a = 46

a= 23

Putting a=23 in a+b=32, we get

23+b=32

b=32-23

b= 9

Hence, two numbers are:

23 and 9