If x = 21/3 + 22/3, then the value of x3 − 6x is

  x 3 -6x  

=  (21/3  + 22/3 )3 - 6( 21/3 + 22/3 )

  =[  2 + 22 + 3 .21/3   . 22/3 (21/3 + 22/3 )  ]   - 6 ( 21/3 + 22/3 )

  =  6 + 6 ( 21/3 + 22/3)  - 6(21/3 + 22/3)

  = 6

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x= 21/3+ 22/3 

x3 = ( 21/3+ 22/3 )3

x3 = 23/3+ 22*3/3

x3 = 21+ 22/9

Now, x-6x =21+ 22/9-6( 21/3+ 22/3 )

                     =2+ 22/9-121/3- 122/3

                     =2+ 22/9-121/3- 122/3

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