Question

How to calculate if x minus 1 by x is equal to 5 then find value of x cube minus 1 by x cube

Answer 1

Answer:

140

Step-by-step explanation:

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

Given

$x - \frac{1}{x} = 5$

So,

${x}^{3} - \frac{1}{ {x}^{3} } = {5}^{3} + 3(5) = 125 + 15 = 140$

Hence, the answer is 140.

Thank you