Quadratic Equation And Inequalities

Let \(\alpha, \beta\) be the roots of the quadratic equation \(x^{2}+\sqrt{6} x+3=0\). Then \(\frac{\alpha^{23}+\beta^{23}+\alpha^{14}+\beta^{14}}{\alpha^{15}+\beta^{15}+\alpha^{10}+\beta^{10}}\) is equal to :