Question

if x = 2-√3
find 1.
$x - \frac{1}{x}$

Answer 1

x=2-√3
1/x=2+√3
x - 1/x = 2 -√3 -2 -√3 =-2√3

Answer 2

Hi...☺

Here is your answer...✌
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$x = 2 - \sqrt{3} \\ \\ \frac{1}{x} = \frac{1}{2 - \sqrt{3} } \\ \\ Rationalising \: \: the \: \: denominator \\ we \: \: get, \\ \\ \frac{1}{x} = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ = \frac{2 + \sqrt{ 3} }{ {2}^{2} - {( \sqrt{3}) }^{2} } \\ \\ = \frac{2 + \sqrt{3} }{4 - 3} \\ \\ = 2 + \sqrt{3}$

Now,

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