MCQ
જો $f(x + ay,\;x - ay) = axy$, તો $f(x,\;y) =$
- A$xy$
- B${x^2} - {a^2}{y^2}$
- ✓$\frac{{{x^2} - {y^2}}}{4}$
- D$\frac{{{x^2} - {y^2}}}{{{a^2}}}$
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
$f(u,v) = \frac{{{u^2} - {v^2}}}{4}$ ==> $f(x,\,y) = \frac{{{x^2} - {y^2}}}{4}$.
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