If $(5\sqrt{5}x^3-3\sqrt{3}y^3)÷ (\sqrt{5}x-\sqrt{3}y) = (Ax^2 + By^2+Cxy)$, then the value of $(3A+B - \sqrt{15}C)$ is:

3

( a - b ) = \(\frac{a^3 - b^3}{a^2 + b^2 + ab }\)

If $(5\sqrt{5}x^3-3\sqrt{3}y^3)÷ (\sqrt{5}x-\sqrt{3}y) = (Ax^2 + By^2+Cxy)$

On comparing the above equation with ( a - b ) = \(\frac{a^3 - b^3}{a^2 + b^2 + ab }\) we can conclude that ,

a = ($ \sqrt{5}$)² = 5

b = ($\sqrt{3}$)² = 3

c = $ \sqrt{5}$ × $\sqrt{3}$ = \(\sqrt {15}\)

So, put them in  $(3A+B - \sqrt{15}C)$ = 3 × 5 + 3  -(\(\sqrt {15}\) × \(\sqrt {15}\)) 

= 18 - 15= 3