Question

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

Answer 1

HEY USER !!

HERE IS UR ANSWER ---

Given ,,

x = 9 - 4√5

1/x = 1/ 9 - 4√5

So, firstly we hv to rationalize the denominator of 1/x.

( 1 / 9 - 4√5 ) × ( 9 + 4√5 / 9 + 4√5)

= 9 + 4√5 / ( 9 )^2 - (4√5)^2

= 9 + 4√5 / 81 - 80

= 9 + 4√5 / 1

= 9 + 4√5

So , we hv to find x - 1/x....

x = 9 - 4√5

1/x = 9 + 4√5

= 9 - 4√5 - ( 9 + 4√5)

= 9 - 4√5 - 9 - 4√5

= - 8√5

HOPE IT HELPS....

Answer 2

Solution :

Given that,

x = 9 - 4√5

⇒ 1/x = 1 / (9 - 4√5)

Rationalising the denominator of RHS,
We get

1/x = 1 × (9 + 4√5) / (9 - 4√5) (9 + 4√5)

= (9 + 4√5) / [ 9² - (4√5)² ]

= (9 + 4√5) / (81 - 80)

= (9 + 4√5) / 1

⇒ 1/x = 9 + 4√5

Now,

x - 1/x = 9 - 4√5 - (9 + 4√5)

= 9 - 4√5 - 9 - 4√5

= - 8√5