MEMO 2011 ekipno problem 1
Dodao/la:
arhiva28. travnja 2012. Find all functions
![f \colon \mathbb R \to \mathbb R](/media/m/4/2/7/4274589bc617b7d9cd7565e617fd02cf.png)
such that the equality
![y^2f(x) + x^2f(y) + xy = xyf(x + y) + x^2 + y^2](/media/m/3/f/8/3f81b0867f6373582d7375b4185fc8b1.png)
holds for all
![x, y \in \Bbb R](/media/m/c/3/8/c386d592c03d772e719bb0956ead7aaa.png)
, where
![\Bbb R](/media/m/0/c/a/0ca3deced1777f29d31572a0e19d110a.png)
is the set of real numbers.
%V0
Find all functions $f \colon \mathbb R \to \mathbb R$ such that the equality $$y^2f(x) + x^2f(y) + xy = xyf(x + y) + x^2 + y^2$$ holds for all $x, y \in \Bbb R$, where $\Bbb R$ is the set of real numbers.
Izvor: Srednjoeuropska matematička olimpijada 2011, ekipno natjecanje, problem 1