Answer:
7
Step-by-step explanation:
[tex]x^2-y^2[/tex] is a difference of squares.
When factoring a difference of squares, you can use this formula [tex]u^2-v^2=(u-v)(u+v)[/tex].
So [tex]x^2-y^2[/tex] can be factored as [tex](x-y)(x+y)[/tex].
So back to the problem:
[tex]x^2-y^2=56[/tex]
Rewriting with a factored left hand side:
[tex](x-y)(x+y)=56[/tex]
We are given x-y=4 so rewriting again with this substitution:
[tex]4(x+y)=56[/tex]
Dividing both sides by 4:
[tex](x+y)=14[/tex]
So we have x+y equals 14.
We are asked to find the average of x and y which is (x+y)/2.
So since x+y=14 , then (x+y)/2=14/2=7.
