Question

if x=√5+2 so find the value of x-1/x

Answer 1

Answer:

4 is the answer of this question

Answer 2

$x = \sqrt{5} + 2$

$\frac{x - 1}{x} \\ \\ = \frac{ \sqrt{5} + 2 - 1}{ \sqrt{5} + 2 } \\ \\ = \frac{ \sqrt{5} + 1}{ \sqrt{5} + 2} \times \frac{ \sqrt{5} - 2 }{ \sqrt{5} - 2} \\ \\ = \frac{( \sqrt{5} + 1)( \sqrt{5} - 2)}{ {( \sqrt{5} )}^{2} - {(2)}^{2} } \\ \\ = \frac{ \sqrt{5}( \sqrt{5} - 2) + 1( \sqrt{5} - 2)}{5 - 4} \\ \\ = \frac{5 - 2 \sqrt{5} + \sqrt{5} - 2 }{1} \\ \\ = {3 - \sqrt{5} }$