Question

If $f(x+\frac{y}{8},x-\frac{y}{8})=xy$ then $f(m,n)+f(n,m)=0$

• A. only when $m=n$
• B. only when $m\ne n$
• C. only when $m=-n$
• D. for all $m$ & $n$

Answer 1

The correct option is D for all $m$ & $n$

Let $x+\frac{y}{8}=m$ and $x-\frac{y}{8}=n$
Solving these we get $x=\frac{m+n}{2},y=4(m-n)$
$\therefore f(m,n)=2(m^2-n^2)$ and $f(n,m)=2(n^2-m^2)=-f(m,n)$
$\therefore f(m,n)+f(n,m)=0$