Let f(x)=3 √(x-2)+√(4-x) be a real valued function. If α and β are respectively the minimum and the maximum values of f, then α^2+2 β^2 is equal to

Let $\displaystyle f(x)=3 \sqrt{x-2}+\sqrt{4-x}$ be a real valued function. If $\displaystyle \alpha$ and $\displaystyle \beta$ are respectively the minimum and the maximum values of $\displaystyle f$, then $\displaystyle \alpha^2+2 \beta^2$ is equal to