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Answer:
x+1/x=6
cubing on both sides
(x+1/x)³=(6)³
x³+2*(x) (1/x)+(1/x)³=216
x³+2+1/x³=216
x³+1/x³=216-2
x³+1/x³=214
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givenx+x1=6
cubing on both sides
\sf \: {(x + \frac{1}{x} )}^{3} = {6}^{3}(x+x1)3=63
\sf \: { {x}^{3} + \frac{1}{{x}^{3}}} + 3(x + \frac{1}{x}) = 216x3+x31+3(x+x1)=216
\sf \: { {x}^{3} + \frac{1}{{x}^{3}}} + 3(6) = 216x3+x31+3(6)=216
\sf \: { {x}^{3} + \frac{1}{{x}^{3}}} + 18 = 216x3+x31+18=216
\sf \: { {x}^{3} + \frac{1}{{x}^{3}}} = 216 - 18x3+x31=216−18
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