Question

x-1/x=5 then x cube -1/x cube =?​

Answer 1

Answer:

GIVEN :-

x - 1/x = 5

TO FIND :-

x³ - 1/x³

SOLUTION :-

We know that -

${(a - b)}^{3} = {a}^{3} - {b}^{3} - 3ab(a - b)$

So ,

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

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

${x}^{3} - \frac{1}{ {x}^{3} } = {(5)}^{3} + 3 \times 5$

${x}^{3} - \frac{1}{ {x}^{3} } = 140$

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