Question

x=2+√3 find the value of x-1/x​

Answer 1

Step-by-step explanation:

this is the answer for your question....

Answer 2

$\sf{x = 2 + \sqrt{3} }$

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

rationalise the denominator

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

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

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

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

now,

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

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

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