Find the value of $$\frac{{{{\left( {0.75} \right)}^3}}}{{1 - 0.75}} + \left[ {0.75 + {{\left( {0.75} \right)}^2} + 1} \right]$$

Solution(By Examveda Team)

$$\eqalign{ & {\text{According to the question,}} \cr & \frac{{{{\left( {0.75} \right)}^3}}}{{1 - 0.75}} + \left[ {0.75 + {{\left( {0.75} \right)}^2} + 1} \right] \cr & \Rightarrow \frac{{{{\left( {0.75} \right)}^3}}}{{1 - 0.75}} + \frac{{{1^3} - {{\left( {0.75} \right)}^3}}}{{1 - 0.75}}\, \cr & \left[ {\because {a^3} - {b^3} = \left( {a - b} \right)\left( {{a^2} + {b^2} + ab} \right)} \right] \cr & \Rightarrow \frac{{{{\left( {0.75} \right)}^3} + 1 - {{\left( {0.75} \right)}^3}}}{{0.25}} \cr & \Rightarrow \frac{1}{{0.25}} \cr & \Rightarrow 4 \cr} $$