Question

If a=1-√3 find (a-1/a)^3​

Answer 1

Step-by-step explanation:

$= \frac{ ({a - 1})^{3} }{ {a}^{3} } \\ = \frac{ ({1 - \sqrt{3} - 1})^{3} }{ { ({1 - \sqrt{3} }) }^{3} } \\ = \frac{ - 3 \sqrt{3} }{1 - 3 \sqrt{3} - 3 \sqrt{3} + 3 \times 3} \\ = \frac{ - 3 \sqrt{3} }{1 + 9 - 6 \sqrt{3} } \\ = \frac{ - 3 \sqrt{3} }{10 - 6 \sqrt{3} }$