Question

X=9-4root 5find the value of root x-1/root x

Answer 1

Answer:

16

Step-by-step explanation:

Given :-

X= 9- 4√5

√x-√1/x = ?

According to question:-

√x-√1/x ------------( Square both the side)

x + 1/x - 2.√x.1/√x

x + 1/x - 2 -----------( equation 1)

Now

x = 9- 4√5

1/x = 1/(9-4√5) ------(rationalising the roots)

= 1 9+4√5

--------- x ------------

9-4√5 9+4√5

= 9+ 4√5

------------

81 - 80

1/x = 9+4√5

From equation 1:-

√x-√1/x = x + 1/x - 2

= (9-4√5) + (9+ 4√5) - 2

= 18 - 2

= 16