Question

If x= 9-4√5 :
find
(a). √x -1/√x
(b). x -1/x

Answer 1

Answer:

If x= 9-4√5 :

find

(a). √x -1/√x

(b). x -1/x

Answer 2

ANSWERS = a => 16 b=> 0

x = 9 - 4√5

a) (√x - ( 1/√x))^2 = √x ^2 - (2.√x.1 / √x ) +( 1 / √x)^2

= x + (1 / x) - 2

x + 1/x = 9 - 4√5 + ( 1 / 9 - 4√5)-2

= 9 - 4√5 + [( 9 + 4√5 )/ (9 ^2 - (4√5)^2) ]-2

= 9 - 4√5 + [( 9 + 4√5) / (81 - 80)] - 2

= 9 - 4 √5 + 9 + 4√5 - 2

= 18 -2

= 16

b) x - (1/x) = 9 - 4√5 - ( 1/ 9 -/4√5)

= 9 - 4√5 - [ 9+ 4√5/ (9^2 - (4√5)^2)]

= 9 - 4√5 - [ (9 + 4√5) / (81 - 80)]

= 9 - 4√5 - 9 - 4√5

= 0