The question is Find all functions f:R→R such that f(x+y)f(x−y)=(f(x)+f(y))2−4x2f(y) Taking x=y=0, we get f(0)2=4f(0)2⟹f(0)=0. Now take x=y which immediately gives 4f(x)2=4x2f(x)⟹f(x)(f(x)−x2)=0⟹f(x)=0 or f(x)=x2 ∀x∈R This was my solution. But I was stunned when I looked at the official solution.
Why do we need to continue to do anything after getting what I got, isn't it sufficient?
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