Question

if x=2-√3 then find x+1/x​

Answer 1

x=2-√3 1/x=2+√3

[if A^m=a+√b,then1/A^m=a-√b or vive versa]

x+1/x=2-√3+2+√3=4 ans

Answer 2

$\rm{x = 2 - \sqrt{3} }$

$\rm \frac{1}{x} = \frac{1}{2 - \sqrt{3} }$

rationalise the denominator

$\rm \frac{1}{x} = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} }$

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

$\rm \frac{1}{x} = \frac{2 + \sqrt{3} }{ 4 - 3}$

$\rm \frac{1}{x} = {2 + \sqrt{3} }$

now,

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

$\fbox{ \rm{x + \frac{1}{x} = 4}}$