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Question

If f(x+y,xy)=xy, then f(x,y)+f(y,x)2 is

A
x
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B
y
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C
0
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D
x+y2
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Solution

The correct option is C 0
Assuming x+y=u, xy=v
x=u+v2, y=uv2

f(x+y,xy)=xy
f(u,v)=(u+v2)×(uv2)
f(u,v)=u2v24
f(u,v)+f(v,u)=u2v24+v2u24f(u,v)+f(v,u)=0
f(x,y)+f(y,x)=0

f(x,y)+f(y,x)2=0

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