Question

if x-1 by x =3 find the value of x to the power of 3- 1 by xto the power of 3

Answer 1

Step-by-step explanation:

$Given: {x} - \frac{1}{x} = 3 \\ \because( {x} - \frac{1}{x})^{3} = {x}^{3} - \frac{1}{ {x}^{3} } - 3x ^{2} \times \frac{1}{x} + 3x \times \frac{1}{ {x}^{2} } \\ \therefore \: (3)^{3} = {x}^{3} - \frac{1}{ {x}^{3} } - 3x + \frac{3}{ {x} } \: \\ \therefore \: 27 = {x}^{3} - \frac{1}{ {x}^{3} } - 3(x - \frac{1}{ {x} } ) \\ \therefore \: 27 = {x}^{3} - \frac{1}{ {x}^{3} } - 3 \times 3 \\ \therefore \: 27 = {x}^{3} - \frac{1}{ {x}^{3} } - 9 \\\therefore \: 27 + 9= {x}^{3} - \frac{1}{ {x}^{3} } \\\therefore \: 36= {x}^{3} - \frac{1}{ {x}^{3} } \\\therefore \: {x}^{3} - \frac{1}{ {x}^{3} } = 36$