If f2x+y8,2x-y8=xy, then fm,n+fn,m=0

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only when m=n

only when m≠n

only when m=-n

for all m and n

answer is D.

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Detailed Solution

Let 2x+y8=α and 2x-y8=β.Then x=α+β4 and y=4α-β.Given f2x+y8,2x-y8=xy∴ fα,β=α2-β2or fm,n+fn,m=m2-n2+n2-m2=0 for all m,n

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