Question

x-1/x=5 then x^3-1/x^3=?

Answer 1

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

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

$x^{3} - (\frac{1}{x})^{3} - 3 . x^{2}. \frac{1}{x} + 3x (\frac{1}{x})^{2}$ = 125

$x^{3} - \frac{1}{x^{3}} - 3 . x + 3 .\frac{1}{x}$ = 125

$x^{3} - \frac{1}{x^{3}} - 3 . x + \frac{3}{x} = 125$

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

$x^{3} - \frac{1}{x^{3}} = 125 +15$

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


Note: (a-b)³ = a³ - b³ +3a²b +3ab²