The first equation is 
(Equation 1)
The second equation is
(Equation 2)
Putting the value of x from equation 1 in equation 2.
we get,


by simplifying the given equation,


Using discriminant formula,


Now the formula for solution 'x' of quadratic equation is given by:


Hence, these are the required solutions.
Let's assume the gemstones are A, B, C, D, E
1. A, B
2. A, C
3. A, D
4. A, E
5. B, C
6. B, D
7. B, E
8. C, D
9. C, E
10. D, E
A: 10 different rings are possible.
Hope this helps. - M
Answer is 1/36...
probability of rolling a 3 is 1/6 so if you do it twice it will be 1/6×1/6=1/36