Question

if X = √7+√6 then find x - 1/x​

Answer 1

Step-by-step explanation:

We have,

$x = \sqrt{7} + \sqrt{6}$

Now,

$\frac{1}{x} = \frac{1}{ \sqrt{7} + \sqrt{6} }$

$\implies \: \frac{1}{x} = \frac{( \sqrt{7} - \sqrt{6} ) }{ (\sqrt{7} + \sqrt{6} )( \sqrt{7} - \sqrt{6} )}$

$\implies \: \frac{1}{x} = \frac{( \sqrt{7} - \sqrt{6} ) }{ 7 - 6 }$

$\implies \: \frac{1}{x} = \frac{( \sqrt{7} - \sqrt{6} ) }{1}$

$\implies \: \frac{1}{x} = \sqrt{7} - \sqrt{6}$

Now,

$x + \frac{1}{x} = \sqrt{7} + \sqrt{6} + \sqrt{7} - \sqrt{6}$

$\implies \: x + \frac{1}{x} = \sqrt{7} + \sqrt{7}$

$\implies \: x + \frac{1}{x} = 2\sqrt{7}$