If $$x = {3^{\frac{1}{3}}} - {3^{ - \frac{1}{3}}}$$   value of $$3{x^3} + 9x$$   is?

Solution (By Examveda Team)

$$\eqalign{ & x = {3^{\frac{1}{3}}} - {3^{ - \frac{1}{3}}} \cr & \Rightarrow x + {3^{ - \frac{1}{3}}} = {3^{\frac{1}{3}}}\,\,\left( {{\text{cubing both sides}}} \right) \cr & \Rightarrow {x^3} + \frac{1}{3} + 3 \times x \times {3^{ - \frac{1}{3}}}\left( {x + {3^{ - \frac{1}{3}}}} \right) = 3 \cr & \Rightarrow {x^3} + \frac{1}{3} + 3 \times x \times {3^{ - \frac{1}{3}}} \times {3^{\frac{1}{3}}} = 3 \cr & \,\,\,\,\,\,\,\,\,\left( {{\text{multiply both sides by 3}}} \right) \cr & \Rightarrow 3{x^3} + 9x = 9 - 1 \cr & \Rightarrow 3{x^3} + 9x = 8 \cr} $$