If 3x² - 9x + 3 = 0, then what is the value of $${\left( {x + \frac{1}{x}} \right)^3}?$$

Solution (By Examveda Team)

$$\eqalign{ & 3{x^2} - 9x + 3 = 0 \cr & 3x\left( {x - 3 + \frac{1}{x}} \right) = 0,\,x + \frac{1}{x} = 3 \cr & \therefore \,{\left( {x + \frac{1}{x}} \right)^3} = {\left( 3 \right)^3} = 27 \cr} $$