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