WBJEE · Maths · Functions
If \(f(x+2 y, x-2 y)=x y\), then \(f(x, y)\) is equal to
- A \(\frac{1}{4} x y\)
- B \(\frac{1}{4}\left(x^2-y^2\right)\)
- C \(\frac{1}{8}\left(x^2-y^2\right)\)
- D \(\frac{1}{2}\left(x^2+y^2\right)\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{8}\left(x^2-y^2\right)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned}\text{Hint: } & x+2 y=a \\ & \frac{x-2 y=b}{2 x=a+b} \\ & 4 y=a-b \end{aligned}\) \(f(a, b)=\left(\frac{a+b}{2}\right)\left(\frac{a-b}{4}\right)=\frac{a^2-b^2}{8}\)
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