Question

if x=9-4√5, find the value of 1/x​

Answer 1

Step-by-step explanation:

hope it helps

answer is given above

Answer 2

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

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

Rationalise the denominator,

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

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

$= \frac{9 + 4 \sqrt{5} }{81 - (16 \times 5)}$

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

$= 9 + 4 \sqrt{5}$

So, x= 9+4√5