Question

x-1/x=1/3 evaluate x³-1/x³

Answer 1

Step-by-step explanation:

Given, (x- 1/x) =1/3 .

So, (x- 1/x)³ = 1/27

=> (x³-1/x³ -3x²×1/x + 3x×1/x²) = 1/27

=> [x³ - 1/x³ -3(x-1/x)] = 1/27

=> [x³ - 1/x³ -3(1/3)] = 1/27

=> [x³- 1/x³ -1] = 1/27

=> x³ - 1/x³ = 1/27 +1

=> x³ - 1/x³ = 28/27

Answer 2

$\huge {\boxed{ \red{Answer}}}$

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

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

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

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

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

${x}^{3} - \frac{1}{ {x}^{3} } = \frac{28}{27}$