(x + ¹/_x)³ = (x³ + ¹/_x³) + 3(x + ¹/_x).

.'. (x + ¹/_x)³ - 3 (x + ¹/_x) = (x³ + ¹/_x³) = 52

So  (x + ¹/_x)³ - 3 (x + ¹/_x) = 52

Now, trick here is to , instead of resolving above equations and getting value of (x + ¹/_x) , its better to apply value from options itself, since it would be faster to get required answer.

So here first option clearly fits into equation 4³ - 3 * 4 = 64 - 12 = 52