Question

if x=2+√3
.
.
then
x^3+1/(x)^3​

Answer 1

Answer:

$x = 2 + \sqrt{3} \\ \frac{1}{x} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } = \frac{2 - \sqrt{3} }{ {2}^{2} - {( \sqrt{3} )}^{2} } = 2 - \sqrt{3} \\ so \: {x}^{3} + \frac{1}{ {x}^{3} } = {(2 + \sqrt{3}) }^{3} + {(2 - \sqrt{3} )}^{3} \\ = 2( {(2)}^{3} + 3(2){ (\sqrt{3} )}^{2} ) \\ = 2(8 + 18) \\ = 2 \times 26 \\ = 52$

Answer 2

Answer:

answer is 52...............