If f(x + ay,;x - ay) = axy, then f(x,;y) is e | vedclass

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Question

(c) Given $f(x + ay,\,x - ay) = axy$&hellip;..$(i)$

Let $x + ay = u$ and $x - ay = v$

Then $x = \frac{{u + v}}{2}$ and $y = \frac{{u - v}}{{2a}}

Vedclass · Accepted Answer

$\frac{{{x^2} - {y^2}}}{4}$

Vedclass · Answer

(c) Given $f(x + ay,\,x - ay) = axy$&hellip;..$(i)$

Let $x + ay = u$ and $x - ay = v$

Then $x = \frac{{u + v}}{2}$ and $y = \frac{{u - v}}{{2a}}$

Substituting the value of $x$ and $y$ in $(i)$, we obtain

$f(u,v) = \frac{{{u^2} - {v^2}}}{4}$ ==> $f(x,\,y) = \frac{{{x^2} - {y^2}}}{4}$.

If $f(x + ay,\;x - ay) = axy$, then $f(x,\;y)$ is equal to

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