Answer:
The difference of two numbers using identity
is 4.
Step-by-step explanation:
Given: The sum of the numbers is 12 and the difference of the squares of the numbers is 48.
To find the difference of two numbers using identity ![(x+y)(x-y)=x^2-y^2](https://tex.z-dn.net/?f=%28x%2By%29%28x-y%29%3Dx%5E2-y%5E2)
Let the two numbers be a and b, then
Given that the sum of the numbers is 12
that is a + b = 12 .........(1)
Also, given the difference of the squares of the numbers is 48.
that is
..........(2)
Using given identity ![(x+y)(x-y)=x^2-y^2](https://tex.z-dn.net/?f=%28x%2By%29%28x-y%29%3Dx%5E2-y%5E2)
We have ![(a+b)(a-b)=a^2-b^2](https://tex.z-dn.net/?f=%28a%2Bb%29%28a-b%29%3Da%5E2-b%5E2)
Substitute the known values, we have,
![12(a-b)=48](https://tex.z-dn.net/?f=12%28a-b%29%3D48)
Divide both side 12 , we have,
![(a-b)=4](https://tex.z-dn.net/?f=%28a-b%29%3D4)
Thus, the difference of two numbers using identity
is 4.