Application Of Derivatives

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