Question 6
Find all functions $ f : \mathbb{R} \to \mathbb{R} $ satisfying the equation
$$ f\left(x^{2}+y^{2}+2f(x y)\right)=\left(f(x+y)\right)^{2}\quad\text{for all }\quad x,y\in\mathbb{R}. $$
$$ f\left(x^{2}+y^{2}+2f(x y)\right)=\left(f(x+y)\right)^{2}\quad\text{for all }\quad x,y\in\mathbb{R}. $$