The value of $$\frac{{5.35 \times 5.35 \times 5.35 + 3.65 \times 3.65 \times 3.65}}{{53.5 \times 53.5 + 36.5 \times 36.5 - 53.5 \times 36.5}}{\text{is:}}$$

Solution (By Examveda Team)

$$\eqalign{ & \frac{{5.35 \times 5.35 \times 5.35 + 3.65 \times 3.65 \times 3.65}}{{53.5 \times 53.5 + 36.5 \times 36.5 - 53.5 \times 36.5}} \cr & = \frac{{{{5.35}^3} + {{3.65}^3}}}{{{{53.5}^2} + {{36.5}^2} - 53.5 \times 36.5}} \cr & = \frac{{\left( {5.35 + 3.65} \right)\left[ {{{\left( {5.35} \right)}^2} + {{\left( {3.65} \right)}^2} - 5.35 \times 3.65} \right]}}{{{{10}^2}\left[ {{{\left( {5.35} \right)}^2} + {{\left( {3.65} \right)}^2} - 5.35 \times 3.65} \right]}} \cr & = \frac{9}{{{{10}^2}}} \cr & = 0.09 \cr} $$