Question

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

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

Answer 1

The correct option is A

$\frac{x^2-y^2}{8}$

Given: $f(x+2y,x-2y)=xy,$
Let $x+2y=p\&x–2y=q$
Solving both of these equation, we get
$x=\frac{p+q}{2}\&y=\frac{p-q}{2}\therefore f(p,q)=\frac{p^2-q^2}{8}\Rightarrow f(x,y)=\frac{x^2-y^2}{8}$