Question

If \( \left(x+\frac{1}{x}\right)=7.5 \), what is the value of \( \left(X^{3}+\frac{1}{X^{3}}\right) \) ? 1. \( 54.25 \) X 2. \( 52.25 \) X \( 3.58 .25 \) \( \times 4525 \)

Answer 1

\(x + \frac{1}{x} = 7.5\)

\((x^3 + \frac{1}{x^3}) = (x + \frac{1}{x})^3 - 3.x.\frac{1}{x}(x + \frac{1}{x})\)

= (7.5)³  - 3(7.5)

= 421.875 - 22.5

= 399.375