if x -1/x =3; then find the value of x3 -1/x3 - Maths - Polynomials

Question

if x -1/x =3; then find the value of x3
-1/x3

Harleen Birdi · Accepted Answer

$We have x - \frac{1}{x} = 3 (1)$ Cubing both sides $(x - \frac{1}{x})^{3} = 3^{3} \Rightarrow x^{3} - (\frac{1}{x})^{3} - 3 x \times \frac{1}{x} (x - \frac{1}{x}) = 27 \Rightarrow x^{3} - \frac{1}{x^{3}} - 3 \times (x - \frac{1}{x}) = 27 \Rightarrow x^{3} - \frac{1}{x^{3}} = 27 + 3 (x - \frac{1}{x}) \Rightarrow x^{3} - \frac{1}{x^{3}} = 27 + 3 \times 3 [Using (1)] \Rightarrow x^{3} - \frac{1}{x^{3}} = 36$