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## Answers

Cubing both the side we get

(x+1/x)^3 = x^3 + (1/x)^3 + 3(x + 1/x)

={sqrt3+1+(sqrt3-1)/2)}^3 = x^3 +(1/x)^3 + 3(sqrt3+1+(sqrt3-1)/2)

={(3sqrt3+1)/2}^3=x^3 + (1/x)^3 + 3{(3sqrt3+1)/2)

={(3sqrt3+1)/2}^3 - {3{(3sqrt3+1)/2)}

= (81sqrt3+1)/8-{(9sqrt3+3)/2}

here "-" sign will change signs after the bracket

taking lcm

(81sqrt3+1-36sqrt3-12)/8

=(45sqrt3-11)/8