Question

if a=2-√3 find value of a-1/a^3

Answer 1

Answer:

$a = 2 - \sqrt{3}$

$\frac{a - 1}{ {a}^{3} } \\ = \frac{2 - \sqrt{3} - 1 }{(2 - \sqrt{3} ) {}^{3} } \\ = \frac{1 - \sqrt{3} }{ {2}^{3} - ( \sqrt{3} ) {}^{3} -3 \times 2 \times \sqrt{3} \times (2 - \sqrt{3} ) } \\ = \frac{1 - \sqrt{3} }{8 - 3 \sqrt{3} - 6 \sqrt{3}(2 - \sqrt{3}) } \\ = \frac{1 - \sqrt{3} }{8 - 3 \sqrt{3} - 12 \sqrt{3} + 18 } \\ = \frac{1 - \sqrt{3} }{26 - 15 \sqrt{3} }$