If the domain of \({\log }_{x-1}\left(\frac{2{x}^{2}-9x+4}{{x}^{2}-4x+5}\right)\) is \((\alpha ,\infty )\) and \({\log }…

If the domain of \({\log }_{x-1}\left(\frac{2{x}^{2}-9x+4}{{x}^{2}-4x+5}\right)\) is \((\alpha ,\infty )\) and \({\log }_{5}\left(18x-{x}^{2}-77\right)\) is \((\beta ,\gamma )\), then the value of \({\alpha }^{2}+{\beta }^{2}+{\gamma }^{2}\) is