Basic operations, simple factors, factor Theorem, Remainder Theorem, Division of polynomials.
If (x3 + 1/x3) = 52, the value of (x + 1/x) is :
(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