If x +1/x sq =83, then find the value of x cube - 1/xcube
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x^2 + 1/x^2 = 83
( x - 1/ x )^2 = x^2 + 1/x^2 - 2 ( x )( 1/x )
( x - 1/x )^2 = 83 - 2
( x - 1/x )^2 = 81
( x - 1/x ) = 9
( x - 1/x )^3 = x^3 - 1/x^3 - 3 ( x ) ( 1/x ) ( X - 1/ x)
9^3 = x^3 - 1/x^3 - 3 ( 9 )
729 = x^3 - 1/x^3 - 27
x^3 - 1/x^3 = 729 + 27
x^3 - 1/x^3 = 756
( x - 1/ x )^2 = x^2 + 1/x^2 - 2 ( x )( 1/x )
( x - 1/x )^2 = 83 - 2
( x - 1/x )^2 = 81
( x - 1/x ) = 9
( x - 1/x )^3 = x^3 - 1/x^3 - 3 ( x ) ( 1/x ) ( X - 1/ x)
9^3 = x^3 - 1/x^3 - 3 ( 9 )
729 = x^3 - 1/x^3 - 27
x^3 - 1/x^3 = 729 + 27
x^3 - 1/x^3 = 756
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