Question

if x= 9- 4 root 5 ,then find x-1/x

Answer 1

Given x = 9 - 4root5.

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

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

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

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

$9 + 4 \sqrt{5}$


Now,

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

                            $= -8 \sqrt{5}$



Hope this helps!

Answer 2

Hi,

Please see the attached file!


Thanks