Problem 3 Let $\mathbb{R}$ be the set of real numbers. Determine all functions $f:\mathbb{R} \rightarrow \mathbb{R}$ such that for all real numbers $x, y,$ the following holds:$$f((f(x) + f(y))^2) = (x + y)f(x + y).$$ Solution 1Solution 1 Solution 2 Solution2 Solution 3 Solution3 Solution 4 Solution4