If f x + y, x - y = xy, then the arithmetic mean of f x , y and f y , x is

Question

If f x + y, x - y = xy, then the arithmetic mean of f x , y and f y , x is, x, y, 0, x 2 - y 2 2

MARKS App · Accepted Answer

Let, x + y = p, x - y = q Then, f p, q = p + q 2 · p - q 2 = p 2 - q 2 4 ∴ f x, y = x 2 - y 2 4 and f y, x = y 2 - x 2 4 A . M . = f x , y + f y , x 2 = x 2 - y 2 4 + y 2 - x 2 4 2 = 0

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