Question

if x-1/x=5 find the value of x3-1/x3

Answer 1

$\frac{x - 1}{x} = 5 \\ = > x - 1 = 5x \\ = > x - 5x = 1 \\ = > - 4x = 1 \\ = > x = - \frac{1}{4} \\ we \: get \: the \: valu \: of \: x \: \\ putting \: the \: value \: of \: x \: in \: \\ = \frac{3x - 1}{3x} \\ = \frac{3 \times ( - \frac{1}{4}) - 1 }{3 \times ( - \frac{1}{4} )} \\ = \frac{ - \frac{3}{4} - 1 }{ - \frac{3}{4} } \\ = \frac{ \frac{ - 3 - 4}{4} }{ - \frac{3}{4} } \\ = \frac{ \frac{ - 7}{4} }{ \frac{ - 3}{4} } \\ = \frac{7}{3}$

Answer 2

x-1/x=5

cubing both sides

(x-1/x)³=125

x³-1/x³ -3(x-1/x)=125

x³-1/x³ -15=125

x³ - 1/x³=140