Let α, β be the roots of the quadratic equation x^2+√ 6 x+3=0. Then (α^23+β^23+α^14+β^14)/(α^15+β^15+α^10+β^10) is equal to

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