Question

if x=9-4√5 , find value of ( i ) x+ 1/x (ii) x-1/x

Answer 1

hey ur answer dude
dfgh☺️

Answer 2

Heya friend,
Here is the answer you were looking for:
$x = 9 - 4 \sqrt{5} \\ \\ \frac{1}{x} = \frac{1}{9 - 4 \sqrt{5} }$

On rationalizing the denominator we get,

$\frac{1}{x} = \frac{1}{9 - 4 \sqrt{5} } \times \frac{9 + 4 \sqrt{5} }{9 + 4 \sqrt{5} } \\ \\ \frac{1}{x} = \frac{9 + 4 \sqrt{5} }{ {(9)}^{2} - {(4 \sqrt{5}) }^{2} } \\ \\ \frac{1}{x} = \frac{9 + 4 \sqrt{5} }{81 - 80} \\ \\ \frac{1}{x} = 9 + 4 \sqrt{5} \\ \\ (i) \\ x + \frac{1}{x} = (9 - 4 \sqrt{5} ) + (9 + 4 \sqrt{5} ) \\ \\ x + \frac{1}{x} = 9 - 4 \sqrt{5} + 9 + 4 \sqrt{5} \\ \\ x + \frac{1}{x} = 18 \\ \\ (ii) \\ x - \frac{1}{x} = (9 - 4 \sqrt{5} ) - (9 + 4 \sqrt{5} ) \\ \\ x - \frac{1}{x} = 9 - 4 \sqrt{5} - 9 - 4 \sqrt{5} \\ \\ x - \frac{1}{x} = - 8 \sqrt{5}$

Hope this helps!!!

Feel free to ask in the comment section if you have any doubt regarding to my answer...

@Mahak24

Thanks...
☺☺