Question

if x=9-4√5 the find x+1/x​

Answer 1

Answer:

18

Step-by-step explanation:

if, x=9-4√5

then,

$\frac{1}{x}$=$\frac {1}{(9-4\sqrt{5} )}$

   = $\frac {1}{(9-4\sqrt{5} )}$ × $\frac{9+4\sqrt{5} }{9+4\sqrt{5}}$   {rationalization}

  =$\frac{9+4\sqrt{5} } {9^{2} - (4\sqrt{5}) ^ {2} }$ (a^2-b^2)

  =${9+4\sqrt{5} }$

so,

x+1/x

=9-4√5+${9+4\sqrt{5} }$

=9+9

=18