If f(x + y,x - y) = xy,, then the arithmetic | vedclass

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(c) Let $x + y = u,\,\,x - y = v$

==> $x = \frac{{u + v}}{2},y = \frac{{u - v}}{2}$,

$	herefore f(u,v) = \left( {\frac{{u + v}}{2}} ight).

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(c) Let $x + y = u,\,\,x - y = v$

==> $x = \frac{{u + v}}{2},y = \frac{{u - v}}{2}$,

$	herefore f(u,v) = \left( {\frac{{u + v}}{2}} ight).\left( {\frac{{u - v}}{2}} ight)$

Now,$\frac{{f(x,y) + f(y,x)}}{2} = \frac{{\left( {\frac{{x + y}}{2}.\frac{{x - y}}{2}} ight) + \left( {\frac{{y + x}}{2}.\frac{{y - x}}{2}} ight)}}{2} = 0$.

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

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