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If \(f(x+2 y, x-2 y)=x y\), then \(f(x, y)\) is equal to
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Verified Answer
The correct answer is:
\(\frac{1}{8}\left(x^2-y^2\right)\)
\(\begin{aligned}\text{Hint: }
& x+2 y=a \\
& \frac{x-2 y=b}{2 x=a+b} \\
& 4 y=a-b
\end{aligned}\)
\(f(a, b)=\left(\frac{a+b}{2}\right)\left(\frac{a-b}{4}\right)=\frac{a^2-b^2}{8}\)
& x+2 y=a \\
& \frac{x-2 y=b}{2 x=a+b} \\
& 4 y=a-b
\end{aligned}\)
\(f(a, b)=\left(\frac{a+b}{2}\right)\left(\frac{a-b}{4}\right)=\frac{a^2-b^2}{8}\)
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