Answer:
The difference of two numbers using identity [tex](x+y)(x-y)=x^2-y^2[/tex] 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 [tex](x+y)(x-y)=x^2-y^2[/tex]
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 [tex]a^2-b^2=48[/tex] ..........(2)
Using given identity [tex](x+y)(x-y)=x^2-y^2[/tex]
We have [tex](a+b)(a-b)=a^2-b^2[/tex]
Substitute the known values, we have,
[tex]12(a-b)=48[/tex]
Divide both side 12 , we have,
[tex](a-b)=4[/tex]
Thus, the difference of two numbers using identity [tex](x+y)(x-y)=x^2-y^2[/tex] is 4.
Answer:
The difference of two numbers is 7.
Step-by-step explanation:
We have given that
The sum of the numbers is 12
x+y = 12
The difference of the squares of the numbers is 48.
x²-y² = 48
We have to find the difference of two numbers.
x-y = ?
Given formula is:
(x+y)(x-y) = x²-y²
Putting values in above formula, we have
(12)(x-y) = 48
x-y = 48 / 12
The difference of two numbers = x-y = 4 which is the answer.
