Sunday, November 29, 2015

functional equations - Find all functions f:mathbbRtomathbbR such that f(a2+b2)=f(a2b2)+f(2ab) for every real a,b

I guessed f(a)=a2 and f(a)=0, but have no idea how to get to the solutions in a good way.



Edit: I did what was suggested:



from a=b=0



f(0)=0



The function is even, because from b=a




f(2a2)=f(2a2).

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