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If f(2x+y/8,2x-y/8)=x y , then f(m , n)+...

If `f(2x+y/8,2x-y/8)=x y` , then `f(m , n)+f(n,m)=0` (a) only when `m=n` (b) only when `m!=n` (c) only when `m=-n` (d) `for all m and n`

A

only when `m = n`

B

only when `m ne n`

C

only when `m = -n`

D

for all m and n

Text Solution

Verified by Experts

The correct Answer is:
D
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
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