If f (x + y, x – y) = xy, then the arithmetic mean of f (x, y) and f ( y, x) is

Let x + y = a and x – y = b⇒x=a+b2 and y=a−b2f (x + y, x – y) = xy⇒f(a,b)=a+b2⋅a−b2=a2−b24∴f(x,y)=x2−y24 and f(y,x)=y2−x24Arithmetic mean of f (x, y) and f (y, x) is zero.