Question

Please solve this fastly

Answer 1

x-1/x=5
cubing in both the sides
(x-1/x)3=(5)3
=x3-1/x3-3.x.1/x(x-1/x)=125
=x3-1/x3-3×5=125
=x3-1/x3=125+15
x3-1/x3= 140





Hope this will work

Answer 2

$(x + \frac{1}{x} ) = 5$
cubing both side
${(x + \frac{1}{x}) }^{3} = {5}^{3}$
using identity
$( {x - y})^{3} = {x}^{3} - {y}^{3} - 3xy(x - y)$
$( {x})^{3} - ( \frac{1}{x} )^{3} - 3 \times x \times \frac{1}{x} (x - \frac{1}{x} ) = 125$
${x}^{3} - \frac{1}{ {x}^{3} } - 3(5) = 125$
${x}^{3 } - \frac{1}{ {x}^{3} } - 15 = 125$
${x}^{3} - \frac{1}{ {x}^{3} } = 125 + 15$
${x}^{3} - \frac{1}{ {x}^{3} } = 140$
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