find the value of x³+ 1/x³, if x = 2+√3
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It is given that , x = 2 - √3
Then 1/x = 1/(2 - √3) = (2+√3)/(4–3) = 2+√3
Now, x - 1/x = 2 - √3 - 2 - √3 = - 2√3
Therefore , x³- 1/x³
= ( x - 1/x )³+ 3 * x * 1/x ( x - 1/x )
= (- 2√3)³+ 3 ( -2√3 )
= - 24√3 - 6√3
= - 30√3
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