The sum of 2 numbers is 6 and the difference between their squares is 12. What are these numbers?

We are given the sum of 2 numbers as 6 and the difference
between their squares as 12.

Let's take the numbers as A
and B.

A^2 - B^2 = 12

A + B =
6

Now A^2 - B^2 = 12

=>
(A + B)(A-B) = 12

=> 6 (A-B) =
12

=> A- B = 2

So we
have A+B = 6 and A-B =2

Add the two 2A = 8 => A =
4

So B = 6-4 =
2

Therefore the two numbers are 2 and
4.