JEE Math Practice Question

If $$\alpha, \beta$$ are the roots of the equation $$ x^{2}-\left(5+3^{\sqrt{\log _{3} 5}}-5^{\sqrt{\log _{5} 3}}\right)x+3\left(3^{\left(\log _{3} 5\right)^{\frac{1}{3}}}-5^{\left(\log _{5} 3\right)^{\frac{2}{3}}}-1\right)=0 $$, then the equation, whose roots are $$\alpha+\frac{1}{\beta}$$ and $$\beta+\frac{1}{\alpha}$$, is :

1. A.$$3 x^{2}-20 x-12=0$$
2. B.$$3 x^{2}-10 x-4=0$$
3. C.$$3 x^{2}-10 x+2=0$$
4. D.$$3 x^{2}-20 x+16=0$$