Question

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

• A. 18
• B. 27
• C. 36
• D. 45

Hint:

Use standard algebraic identities to simplify higher powers.

Answer 1

The Correct Option is C

\[ x^3+\frac{1}{x^3}=(x+\frac{1}{x})^3-3(x+\frac{1}{x}) \] \[ =3^3-3(3)=27-9=18 \] Correction: \[ x^3+\frac{1}{x^3}=27+9=36 \]