if 4x2 3y2 2x2 5y2 12 19 then x y, Ratio & Proportion, General Mathematics

Question:If `(4x^2 - 3y^2) : (2x^2 + 5y^2) = 12 : 19`, then `x : y` is :

A `2 : 3` 
B `1 : 2` 
C `3 : 2` 
D `2 : 1`

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+ AnswerC

+ Explanation`(4x^2 - 3y^2)/(2x^2 + 5y^2) = 12/19`
 
 `iff``19(4x^2 - 3y^2) = 12(2x^2 + 5y^2)`

 `iff``(76x^2 - 24x^2) = (60y^2 + 57y^2)`

 `iff``52x^2 = 117y^2`

 `iff``4x^2 = 9y^2`

 `iff``x^2/y^2 = 9/4`

 `iff``x/y = 3/2`.

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