If (4x2 - 3y2) : (2x2 + 5y2) = 12 : 19, then x : y is

Answer: Option C

$$\begin{array}{rl}& \text{ = }\frac{4x^2-3y^2}{2x^2+5y^2}=\frac{12}{19}\\ & \Rightarrow 19\left(4x^2-3y^2\right)=12\left(2x^2+5y^2\right)\\ & \Rightarrow 76x^2-57y^2=24x^2+60y^2\\ & \Rightarrow 52x^2=117y^2\\ & \Rightarrow 4x^2=9y^2\\ & \Rightarrow \frac{x^2}{y^2}=\frac{9}{4}\\ & \Rightarrow {\left(\frac{x}{y}\right)}^2={\left(\frac{3}{2}\right)}^2\\ & \Rightarrow \frac{x}{y}=\frac{3}{2}\\ & \therefore x:y=3:2\end{array}$$