Question

if x =
$\sqrt{10} + 3$
then find
$x - \frac{1}{x}$
​

Answer 1

$x = \sqrt{10} + 3$

$\frac{1}{x} = \frac{1}{ \sqrt{10} + 3 }$

$⇒ \frac{1}{x} = \frac{1( \sqrt{10} - 3)}{ (\sqrt{10} + 3)( \sqrt{10} - 3) }$

$⇒ \frac{1}{x} = \frac{ \sqrt{10} - 3 }{( \sqrt{10} )^{2} - {3}^{2} }$

$⇒ \frac{1}{x} = \frac{ \sqrt{10} - 3}{10 - 9}$

$⇒ \frac{1}{x} = \frac{ \sqrt{10} - 3 }{1}$

$\therefore \frac{1}{x} = \sqrt{10} - 3$

$\bold{ x - \frac{1}{x} }$

$= \sqrt{10} + 3 - ( \sqrt{10} - 3)$

$= \sqrt{10} + 3 - \sqrt{10 } + 3$

$= 6$

$\sf \green{Hence, the \: value \: of \:( x - \frac{1}{x}) \: is \: 6.}$