Interesting Question. I have a solution that doesn't involve trig. There may be a way doing this using trig, but I'm not sure how.
First off we have
Factorising gives us
Since x is a positive integer, is also an integer. This means must also be an integer (but only if n > 1)
Now we note that the prime factorisation of .
Because is an integer only if n > 1, we can rule out the prime factor 41 as a possible value for x (it doesn't have a power > 1). This means x = 7. Logically, is 41 (substitute 7 into this to prove it to yourself)
Now divide both sides by 41 and substitute x = 7 to get
Clearly n = 4.
So we now we have x = 7 and n = 4. The answer to the question is B - 11.