Let e_1 and e_2 be two distinct roots of the equation x^2-a x+2=0. Let the sets {a ∈ R: e_1. and e_2 are the eccentricities of hyperbolas }=(α, β),…

Let $\displaystyle e_1$ and $\displaystyle e_2$ be two distinct roots of the equation $\displaystyle x^2-a x+2=0$. Let the sets $\displaystyle \left\{a \in \mathbb{R}: e_1\right.$ and $\displaystyle e_2$ are the eccentricities of hyperbolas $\displaystyle \}=(\alpha, \beta)$, and $\displaystyle \left\{a \in \mathbb{R}: e_1\right.$ and $\displaystyle e_2$ are the eccentricities of an ellipse and a hyperbola, respectively $\displaystyle \}=(\gamma, \infty)$. Then $\displaystyle \alpha^2+\beta^2+\gamma^2$ is equal to: