Let \(\alpha, \beta\) be the roots of the quadratic equation \(x^2+\sqrt{6} x+3=0\). Then \(\frac{{\alpha }^{23}+{\beta …

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

[JEE Main 2023, 12 Apr (Shift 1)]