Question 41
Find all quadruples of real numbers $(a, b, c, d)$ satisfying the system of equations
$$
\begin{cases}
(b+c+d)^{2010} = 3a \\
(a+c+d)^{2010} = 3b \\
(a+b+d)^{2010} = 3c \\
(a+b+c)^{2010} = 3d.
\end{cases}
$$
$$
\begin{cases}
(b+c+d)^{2010} = 3a \\
(a+c+d)^{2010} = 3b \\
(a+b+d)^{2010} = 3c \\
(a+b+c)^{2010} = 3d.
\end{cases}
$$