JEE Math Practice Question

Let $$\alpha, \beta ; \alpha>\beta$$, be the roots of the equation $$x^2-\sqrt{2} x-\sqrt{3}=0$$. Let $$\mathrm{P}_n=\alpha^n-\beta^n, n \in \mathrm{N}$$. Then $$(11 \sqrt{3}-10 \sqrt{2}) \mathrm{P}_{10}+(11 \sqrt{2}+10) \mathrm{P}_{11}-11 \mathrm{P}_{12}$$ is equal to

1. A.$$10 \sqrt{3} \mathrm{P}_9$$
2. B.$$11 \sqrt{3} \mathrm{P}_9$$
3. C.$$11 \sqrt{2} \mathrm{P}_9$$
4. D.$$10 \sqrt{2} \mathrm{P}_9$$