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Basic operations, simple factors, factor Theorem, Remainder Theorem, Division of polynomials.

If (x3 + 1/x3) = 52, the value of (x + 1/x) is :

Option:
A. 4
B. 3
C. 6
D. 13
Answer: A . 4

Justification:

(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

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