If (135√5x² - 2√2y³) ÷ (3√5x - √2y) = Ax² + By² + $$\sqrt {10} $$ Cxy, then the value of (A + B - 9C) is:

Solution (By Examveda Team)

$$\eqalign{ & \left( {135\sqrt 5 {x^3} - 2\sqrt 2 {y^3}} \right) \div \left( {3\sqrt 5 x - \sqrt 2 y} \right) = A{x^2} + B{y^2} + \sqrt {10} Cxy \cr & \Rightarrow \frac{{{{\left( {3\sqrt 5 x} \right)}^3} - {{\left( {\sqrt 2 y} \right)}^3}}}{{3\sqrt 5 x - \sqrt 2 y}} = A{x^2} + B{y^2} + \sqrt {10} Cxy \cr & \Rightarrow \frac{{\left( {3\sqrt 5 x - \sqrt 2 y} \right)\left( {45{x^2} + 2{y^2} + 3\sqrt {10} xy} \right)}}{{\left( {3\sqrt 5 x - \sqrt 2 y} \right)}} = A{x^2} + B{y^2} + \sqrt {10} Cxy \cr & {\text{Comparison both side,}} \cr & A = 45,\,B = 2,\,C = 3 \cr & A + B - 9C = \left( {45 + 2 - 27} \right) \cr & A + B - 9C = 20 \cr} $$