Question

x-1/x=1/3 evaluate x3-1/x3

Answer 1

Question:-

If $x - \frac{1}{x} = \frac{1}{3}$ then, evaluate ${x}^{3} - \frac{1}{ {x}^{3} }$

Solution:-

Given,

$x - \frac{1}{x} = \frac{1}{3}$

Cubing on both sides

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

${x}^{3} - \frac{1}{ {x}^{3} } - 3 \times x \times \frac{1}{x} (x - \frac{1}{x} ) =( { \frac{1}{3} })^{3}$

${x}^{3} - \frac{1}{ {x}^{3} } - 3( \frac{1}{3} ) = \frac{1}{27}$

${x}^{3} - \frac{1}{ {x}^{3} } = \frac{1}{27}$