If (5√5x³ - 81√3y³) ÷ (√5x - 3√3y) = (Ax² + By² + Cxy), then the value of (6A + B - $$\sqrt {15} $$ C) is:

Solution (By Examveda Team)

$$\eqalign{ & 5\sqrt 5 {x^3} - 81\sqrt 3 {y^3} \div \sqrt 5 x - 3\sqrt 3 y = \left( {A{x^2} + B{y^2} + Cxy} \right) \cr & \Rightarrow \frac{{{{\left( {\sqrt 5 x} \right)}^3} - {{\left( {3\sqrt 3 y} \right)}^3}}}{{\sqrt 5 x - 3\sqrt 3 y}} = A{x^2} + B{y^2} + Cxy \cr & \Rightarrow \frac{{\left( {\sqrt 5 x - 3\sqrt 3 y} \right)\left( {5{x^2} + 27{y^2} + 3\sqrt {15} xy} \right)}}{{\sqrt 5 x - 3\sqrt 3 y}} = A{x^2} + B{y^2} + Cxy \cr & \Rightarrow 5{x^2} + 27{y^2} + 3\sqrt {15} xy = A{x^2} + B{y^2} + Cxy \cr & \Rightarrow {\text{ Comprison Coefficient}} \cr & A = 5,\,B = 27,\,C = 3\sqrt {15} \cr & \left( {6A + B - \sqrt {15} C} \right) = 6 \times 5 + 27 - 45 \cr & = 30 + 27 - 45 \cr & = 12 \cr} $$