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If $x - 1/ x = 3$ , then the value of $x^{3} - 1/ x^{3}$ is:

Competition practiceAlgebra

A27
B30
C36
D33

Step-by-Step Solution

Cube both sides:

(x - 1/ x)^{3} = x^{3} - 1/ x^{3} - 3 (x - 1/ x)

, so

27 = (x^{3} - 1/ x^{3}) - 3 (3) = (x^{3} - 1/ x^{3}) - 9

. Hence

x^{3} - 1/ x^{3} = 27 + 9 = 36

.

Answer: C) 36

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