If \( \Large x + \frac{1}{x} = 5 \), then the value of \( \Large x^{3} + \frac{1}{x^{3}} \) is ---


A) 125

B) 110

C) 45

D) 75

Correct Answer:
B) 110

Description for Correct answer:
\( \Large (x + \frac{1}{x})^{3} = (x^{3} + \frac{1}{x^{3}}) + 3(x + \frac{1}{x}) \)

\( \Large (5)^{3} = (x^{3} + \frac{1}{x^{3}}) + 15 \)

\( \Large \therefore x^{3} + \frac{1}{x^{3}} = 125 - 15 = 110 \)

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