Question

If (4x²–3y²):(2x²+5y²)=12:19,find x:y

Answer 1

We know that ,
If a : b = c : d then a, b , c ,d are in proportion.

a × d = b × d

or

Product of extrems = product of
means

Now ,

( 4x² - 3y²) : ( 2x² + 5y² ) = 12 : 19

( 4x² - 3y² ) 19 = ( 2x² + 5y² )12

76x² - 57y² = 24x² + 60y²

76x² - 24x² = 60y² +57y²

52x² = 117y²

x² / y² = 117 / 52

( x/ y )² = ( 13 × 9 ) / ( 13 × 4 )

= 9 / 4

( x / y )² = ( 3 / 2 )²

Therefore ,

x / y = 3 / 2

x : y = 3 : 2