



 
Nazrul, The most straightforward way, not needing any specialized algebraic tricks, is to substitute u = x^{3} and get u + 1/u = 18 sqrt(3) which is equivalent to the quadratic u^{2}  18 sqrt(3) + 1 = 0 which may be solved by standard means. There are also many specialized tricks for problems of this sort. You can find out about these in books intended for math competition training. Herman, Kucera and Simsa' s book on "Equations and Good Hunting! RD
 


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