Question

If x = 9-4 root 5 then find
X + 14 by x

Answer 1

x=9-4√5

x+14/x=127+56√5

hope it helpszz..

Answer 2

Given:

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

To find:

$\frac{x+14}{x}$

Solution:

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

Using rationalization

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

$\frac{1}{x}=\frac{9+4\sqrt 5}{9^2-(4\sqrt 5)^2}$

Using identity

$(a+b)(a-b)=a^2-b^2$

$\frac{1}{x}=\frac{9+4\sqrt 5}{81-80}=9+4\sqrt 5$

$\frac{x+14}{x}$

Substitute the values

$(9-4\sqrt 5+14)\times (9+4\sqrt 5)$

$(23-4\sqrt{5})(9+4\sqrt 5)$

$207+92\sqrt 5-36\sqrt 5-80$

$127+56\sqrt 5$

$\frac{x+14}{x}=127+56\sqrt{5}$