Question

if √x =9+4√5 find the value of √x-1/√x​

Answer 1

Given

$\tt \: x = 9 + 4 + \sqrt{5}$

$\boxed{ \tt=> \: \dfrac{1}{x} = \dfrac{1}{9 + 4 + \sqrt{5} } \times \dfrac{9 - 4 \sqrt{5} }{9 - 4 \sqrt{5}}}$

$\boxed{\sf=> \: \dfrac{1}{x} = 9 - 4 \sqrt{5}}$

Let y :-

$\boxed{\tt \sqrt{x} - \frac{1}{ \sqrt{x} }}$

Squaring both Sides :-

$\boxed{ \sf=> \: y {}^{2} \:= 9 + 4 + \sqrt{5} \: 9 + 4 + \sqrt{5} \: - 2}$

$\red{ \boxed{ \sf \: y \: = + 4 \: , \: - 4}}$

$\rule{190pt}{2pt}$

So the Value comes +4 , -4