Question

if
$\frac{x {}^{2} + y {}^{2} }{x {}^{2} - y {}^{2} } = \frac{17}{8}$
, then the value of x:y is
a=3:5
b=5:3
c=3:8
d=5:8

Answer 1

Given -

( x² + y² ) / ( x² - y² ) = 17 / 8

Cross - multiplication

8 ( x² + y² ) = 17 ( x² - y² )

8x² + 8y² = 17x² - 17y²

8x² - 17x² = - 17y² - 8y²

- 9x² = - 25y²

9x² = 25y²

x² / y² = 25 / 9

x / y = √ ( 25 / 9 )

x / y = 5 / 3

x : y = 5 : 3

Hence, b) option is correct.

^^"