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IF (x-y)f(x+y)-(x+y)f(x-y)=4xy(x+y)(x-y)for all x,y find f(x).

IF (x-y)f(x+y)-(x+y)f(x-y)=4xy(x+y)(x-y)for all x,y find f(x).

Grade:11

1 Answers

Vijay Mukati
askIITians Faculty 2590 Points
8 years ago
Dear Student,

we can write it as f(x+y/(x+y) – f(x-y)/ (x-y) = 4xy = (x+y)2 – (x-y)2
f(x+y/(x+y) – (x+y)2 =f(x-y)/ (x-y) – (x-y)2 = k (say)
Now replace x by (x+y)/2 and y by (x-y)2

You will get the answer from here.

Thanks.

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