Question

If x=3+√8 find the value of x³-(1/x)³​

Answer 1

Given :  x  = 3  +  √8

To find : x³-(1/x)³​

Solution:

x  = 3  +  √8

1/x  =  1/(3 + √8)   =  3 - √8

x³-(1/x)³​

= (3  +  √8)³  - (3 - √8)³

= 27 + 8√8  + 9√8(3 + √8)  -  (  27 - 8√8   - 9√8(3 - √8)

= 16√8  + 9√8 (6)

= 70√8

Another way

x³-(1/x)³​   = (x - 1/x) (x²  + 1/x²  + 1)

=  (x - 1/x)  ( (x - 1/x)² + 2 + 1)

(x - 1/x) = 3 + √8 - (3 - √8) = 2√8

= ( 2√8) (   (2√8)² + 2 + 1)

=  ( 2√8) (32 + 3)

= 70√8

x³-(1/x)³​ = 70√8

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