Question

if x=2+√3 , find the value of
${x}^{3} + \frac{1}{ {x}^{3} }$

Answer 1

given,x=2+√3
so,(2+√3)^3=8+3√3+12√3+18=26+15√3 _(1)
now 1/(2+√3)^3=1/(26+15√3)=1/26+15√3 × 26-15√3/26-15√3=26-15√3/676-675=26-15√3 _(2)
now add (1) and (2)
26+15√3+26-15√3=52
thank u, hope it helped u!