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

Solution (By Examveda Team)

$$\eqalign{ & \left( {5\sqrt 5 {x^3} - 3\sqrt 3 {y^3}} \right) \div \left( {\sqrt 5 x - \sqrt 3 y} \right) = A{x^2} + B{y^2} + Cxy \cr & 3A - B - \sqrt {15} C = ? \cr & \frac{{{{\left( {\sqrt 5 x} \right)}^3} - {{\left( {\sqrt 3 x} \right)}^3}}}{{\sqrt 5 x - \sqrt 3 y}} = A{x^2} + B{y^2} + Cxy \cr & 5{x^2} + 3{y^2} + \sqrt {15} xy \cr & A = 5,\,B = 3,\,C = \sqrt {15} \cr & 3A - B - \sqrt {15} C \cr & = 3 \times 5 - 3 - \sqrt {15} \times \sqrt {15} \cr & = - 3 \cr} $$