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

Solution(By Examveda Team)

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