If `f(2x+y/8,2x-y/8)=x y` , then `f(m , n)=0` only when `m=n` only when `m!=n` `on l yw h e nm=-n` (d) `fora l lma n dn`

Options

A. only when `m = n`
B. only when `m ne n`
C. only when `m = -n`
D. for all m and n

Answer

D

Explanation

Let `2x+(y)/(8)=alpha" and " 2x-(y)/(8)=beta.`
Then ` x=(alpha+beta)/(4) and y=4(alpha-beta).`
Given `f(2x+(y)/(8), 2x-(y)/(8))=xy`
` :. f(alpha, beta)=alpha^(2)-beta^(2)`
`or f(m,n)+f(n,m)=m^(2)-n^(2)+n^(2)-m^(2)=0` for all m,n