Question

14x2 – 3y2) : (2x2 + 5y2) = 12 : 19, find x : y.​

Answer 1

Answer:

$\large{\underline{\boxed{\sf x:y = \sqrt{117} : \sqrt{242}}}}$

Step-by-step explanation:

Given that;

(14x² - 3y²) : (2x² + 5y²) = 12 : 19

We can write it as ;

$\sf \frac{14x {}^{2} - 3y {}^{2} }{2x {}^{2} + 5y {}^{2} } = \frac{12}{19} \\ \\ \bf on \: cross - multiplying : \\ \\ \sf 19(14x {}^{2} - 3y {}^{2} ) = 12(2x {}^{2} + 5y {}^{2}) \\ \\ \sf 266x {}^{2} - 57y {}^{2} = 24x {}^{2} + 60y {}^{2} \\ \\ \sf 266x {}^{2} - 24x {}^{2} - 57y {}^{2} - 60y {}^{2} = 0 \\ \\ \sf 242x {}^{2} - 117y {}^{2} = 0 \\ \\ \sf 242x {}^{2} = 117y^{2} \\ \\ \sf \frac{ {x}^{2} }{ {y}^{2}} = \frac{117}{242} \\\\ \sf ( \frac{x}{y} ) {}^{2} = \frac{117}{242} \\ \\ \sf \frac{x}{y} = \sqrt{ \frac{117}{242} }$

Thus,

x : y = √117 : √242