Question

If $ f(x+2y,x,x-2y)=xy, $ then $ f(x,y) $ equals

• A. $ \frac{{{x}^{2}}-{{y}^{2}}}{8} $
• B. $ \frac{{{x}^{2}}-{{y}^{2}}}{4} $
• C. $ \frac{{{x}^{2}}+{{y}^{2}}}{4} $
• D. $ \frac{{{x}^{2}}-{{y}^{2}}}{2} $

Answer 1

Answer: (A)

We have, $ f(x+2y,x-2y)=xy $ ... (i) Let $ x+2y=u $ and $ x-2y=v $ Then, $ x=\frac{u+v}{2} $ and $ y=\frac{u-v}{4} $ Substituting the values of $ x $ and y in Eq. (i), we obtain $ f(u,v)=\frac{{{u}^{2}}-{{v}^{2}}}{8}\Rightarrow f(x,y)=\frac{{{x}^{2}}-{{y}^{2}}}{8} $