The difference between the squares of two numbers is 39 and the sum of these two numbers is 13. What are those numbers?

Correct option is C

Given:

The difference between the squares of two numbers = 39

The sum of these two numbers = 13

Formula Used:

​$$a^2 - b^2 = (a + b)(a - b)$$​​

Solution:

Let the two numbers be a and b.

Given a$$^2 - b^2$$​= 39 and a + b = 13:

​$$a^2 - b^2 = (a + b)(a - b)$$​​

39 = 13 × (a - b)

​$$a - b = \frac{39}{13} = 3$$​​

a - b = 3  , a + b = 13

Adding these two equations:

(a + b) + (a - b) = 13 + 3

2a = 16

a = 8

Substituting a = 8 into a + b = 13:

8 + b = 13

b = 5

The two numbers are 8 and 5.