NMO试题函数部分

hbghlyj

求所有$f:\mathbf{R}\to\mathbf{R},\forall x,y \in \mathbf{R}$,有\[\left(f\left(x\right)+xy\right)f\left(x-3y\right)+\left(f\left(y\right)+xy\right)f\left(3x-y\right)=\left(f\left(x+y\right)\right)^2\]