Question

if x=9-4√5,then find the value of x^3-1/x^3

Answer 1

Hi ,

x = 9 - 4√5 ----( 1 )

1/x = 1 / ( 9 - 4√5 )

= ( 9 + 4√5 ) / [ ( 9 - 4√5 ) ( 9 + 4√5 )

= ( 9 + 4√5 ) / [ 9² - ( 4√5 )² ]

= ( 9 + 4√5 ) / [ 81 - 80 ]

= 9 + 4√5 ---( 2 )

x - 1/x = 9 - 4√5 - ( 9 + 4√5 )

= 9 - 4√5 - 9 - 4√5

= -8√5 ---( 3 )

x³ - 1/x³ = ( x - 1/x )³ - 3( x - 1/x )

= ( - 8√5 )³ - 3 × ( - 8√5 )

= ( -8√5 ) [ ( - 8√5 )² - 3 ]

= ( -8√5 ) [ 320 - 3 ]

= ( -8√5 ) × 317

= - 2536√5

I hope this helps you.

:(

Answer 2

Answer:

=(9+4√5)/(9-4√5)(9+4√5)

=(9+4√5)/[9²-(4√5)]

=(9+4√5)/(81-80)

=(9+4√5)

=x-1/x=9-4√5-(9+4√5)

=9-4√5- 9-4√5

=-8√5

=x³-1/x³=(x-1/x)³-3(x-1/x)

=(-8√5)[(-8√5)²-3]

=(-8√5)(320-3)

=(-8√5)*317

=2536√5

Step-by-step explanation:

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