Question

(4x2 - 3y2) : (2x2 + 5y2) = 12: 19, find x : y.​

Answer 1

Answer:

$\large{\underline{\boxed{\sf x:y = \sqrt{117} : \sqrt{52}}}}$

Step-by-step explanation:

Given that;

(4x² - 3y²) : (2x² + 5y²) = 12 : 19

We can write it as ;

$\sf \frac{4x {}^{2} - 3y {}^{2} }{2x {}^{2} + 5y {}^{2} } = \frac{12}{19} \\ \\ \bf on \: cross - multiplying : \\ \\ \sf 19(4x {}^{2} - 3y {}^{2} ) = 12(2x {}^{2} + 5y {}^{2}) \\ \\ \sf 76x {}^{2} - 57y {}^{2} = 24x {}^{2} + 60y {}^{2} \\ \\ \sf 76x {}^{2} - 24x {}^{2} - 57y {}^{2} - 60y {}^{2} = 0 \\ \\ \sf 52x^{2} - 117y {}^{2} = 0 \\ \\ \sf 52x {}^{2} = 117y^{2} \\ \\ \sf \frac{ {x}^{2} }{ {y}^{2}} = \frac{117}{52} \\\\ \sf ( \frac{x}{y} ) {}^{2} = \frac{117}{52} \\ \\ \sf \frac{x}{y} = \sqrt{ \frac{117}{52} }$

Thus,

x : y = √117 : √52

Answer 2

Answer:

( 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

Step-by-step explanation: