Question

if a=9-4√5 find the value of a^3-1/a^3

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Answer 1

Answer:

- 2536√5

Step-by-step explanation:

Given :

a = 9 - 4√5

Then

1/a = 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

Now,

a - 1/a = 9 - 4√5 - ( 9 + 4√5 )

= 9 - 4√5 - 9 - 4√5

= -8√5

a³ - 1/a³ = ( a - 1/a)³ - 3(a - 1/a )

= ( - 8√5 )³ - 3 × ( - 8√5 )

= ( -8√5 ) [ ( - 8√5 )² - 3 ]

= ( -8√5 ) [ 320 - 3 ]

= ( -8√5 ) × 317

= - 2536√5

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