The value of $$\frac{5.71 × 5.71 × 5.71 - 2.79 × 2.79 × 2.79}{5.71 × 5.71 + 5.71 × 2.79 + 2.79 × 2.79}$$       is :

A. 2.82

B. 2.92

C. 8.5

D. 8.6

Answer: Option B

Solution(By Examveda Team)

Given expression :
$$\eqalign{ & \frac{{{{\left( {5.71} \right)}^3} - {{\left( {2.79} \right)}^3}}}{{{{\left( {5.71} \right)}^2} + 5.71 \times 2.79 + {{\left( {2.79} \right)}^2}}} \cr & = \left( {\frac{{{a^3} - {b^3}}}{{{a^2} + ab + {b^2}}}} \right) \cr & = \frac{{\left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right)}}{{\left( {{a^2} + ab + {b^2}} \right)}} \cr & = \left( {a - b} \right) \cr & = \left( {5.71 - 2.79} \right) \cr & = 2.92 \cr} $$