if x^2 – y^2 = x- y and x<y, what is the average (arithmetic mean) of x and y?

A) 0
B) 1/2
C) 1
D) x/2
E) y/2

Factor:

x^2-y^2=x-y

(x+y)(x-y)=x-y

Now divide by x-y:

x+y=1

The arithmetic mean of 2 numbers is their sum divided by 2. Since you know the sum of x and y is 1, you know their arithmetic mean is \dfrac{1}{2}.

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