Question 9
Find the largest possible value of $\alpha^4+\beta^4+\gamma^4$ among all possible sets of numbers $(\alpha,\beta,\gamma)$ that satisfy the equations
$$\begin{aligned}\alpha+\beta+\gamma&=2,\\\alpha^2+\beta^2+\gamma^2&=14,\\\alpha^3+\beta^3+\gamma^3&=20.\end{aligned}$$
$$\begin{aligned}\alpha+\beta+\gamma&=2,\\\alpha^2+\beta^2+\gamma^2&=14,\\\alpha^3+\beta^3+\gamma^3&=20.\end{aligned}$$