Question

please answer th8s question raisins urgent , brainly experts please answer fast its urgent.....

Answer 1

$Given : x = 9 - 4 \sqrt{5}$.

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

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

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

$= \ \textgreater \ 9 + 4 \sqrt{5}$

Now,

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

$= \ \textgreater \ 9 + 9$

$= \ \textgreater \ 18$

On Squaring both sides, we get

$= \ \textgreater \ (x + \frac{1}{x} )^2 = (18)^2$

$= \ \textgreater \ x^2 + \frac{1}{x^2} + 2 = 324$

$= \ \textgreater \ x^2 + \frac{1}{x^2} = 324 - 2$

[tex]= \ \textgreater \ x^2 + \frac{1}{x^2} = 322. [/tex]




Hope this helps!