If $$\left( {0.4x + \frac{1}{x}} \right) = 5,$$    what is the value of $$\left( {0.064{x^3} + \frac{1}{{{x^3}}}} \right)?$$

Solution (By Examveda Team)

$$\eqalign{ & \left( {0.4x + \frac{1}{x}} \right) = 5 \cr & {\text{cube both side}} \cr & {\left( {0.4x} \right)^3} + \frac{1}{{{x^3}}} + 3\left( {0.4x + \frac{1}{x}} \right) \times \left( {0.4x} \right)\left( {\frac{1}{x}} \right) = {\left( 5 \right)^3} \cr & 0.064{x^3} + \frac{1}{{{x^3}}} + 3\left( 5 \right)\left( {0.4} \right) = 125 \cr & 0.064{x^3} + \frac{1}{{{x^3}}} + 6 = 125 \cr & 0.064{x^3} + \frac{1}{{{x^3}}} = 119 \cr} $$