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:
Answer & explanation
Correct answer: option 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