Let the set of all positive values of λ, for which the point of local minimum of the function (1+x(λ^2-x^2)) satisfies (x^2+x+2)/(x^2+5 x+6)<0, be…

Let the set of all positive values of $\displaystyle \lambda$, for which the point of local minimum of the function $\displaystyle \left(1+x\left(\lambda^2-x^2\right)\right)$ satisfies $\displaystyle \frac{x^2+x+2}{x^2+5 x+6}<0$, be $\displaystyle (\alpha, \beta)$. Then $\displaystyle \alpha^2+\beta^2$ is equal to $\displaystyle \_\_\_\_$.