Question

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

Answer 1

$2\sqrt{5}$

Step-by-step explanation:

 given,

$x=9-4\sqrt{5}$

    find the value of

   $=\sqrt{x}+1/\sqrt{x}$

$=\left ( \left ( \sqrt{x}+1/\sqrt{x}\right )^{2} \right )^{1/2}$

$=\left ( \sqrt{x}^{2} +2\sqrt{x}\times 1/\sqrt{x}+1/\sqrt{x}^{2}\right )^{1/2}$

$=\left ( x+2+1/x \right )^{1/2}$

$=(9-4\sqrt{5}+2+1/\left ( 9-4\sqrt{5} \right )\times \left ( 9+4\sqrt{5} \right )/\left ( 9+4\sqrt{5} \right))^{1/2}$$=\left ( 9-4\sqrt{5}+2+9+4\sqrt{5} \right )^{1/2}$

$=(9+2+9)^{1/2}$

$=2\sqrt{5}$