Question

if x=2-√3,find the value of (x-1/x)^3

Answer 1

$x = 2 - \sqrt{3 }$

$1 \div x = 1 \div 2 - \sqrt{3}$

rationkasing denominator

$1 \div 2 - \sqrt{3 \times 2 + \sqrt{3} } \div 2 + \sqrt{3}$

$2 + \sqrt{3 \div {2 }^{2} } - { \sqrt{3 =} }^{2}$

$2 + \sqrt{3 \div 4 - 3}$

$2 + \sqrt{3}$

$x - 1 \div x = 2 - \sqrt{3 - (2 + \sqrt{3)} }$

$2 - \sqrt{3 - 2 - \sqrt{3} }$