1.
Let α,β\alpha, \beta be the roots of the quadratic equation x2+6x+3=0x^2 + \sqrt{6} x + 3 = 0. Then α23+β23+α14+β14α15+β15+α10+β10\dfrac{\alpha^{23} + \beta^{23} + \alpha^{14} + \beta^{14}}{\alpha^{15} + \beta^{15} + \alpha^{10} + \beta^{10}} is equal to