Question

6x square + 6y square=13xy, x:y=?

Answer 1

6x² + 6y² = 13xy


6x² - 13xy + 6y² = 0


=> 6x² - 4xy - 9xy + 6y² = 0

=> 2x(3x - 2y) -3y(3x - 2y) = 0

=> (2x - 3y)(3x - 2y). = 0

=> 2x - 3y = 0/(3x - 2y)

=> 2x - 3y = 0
=> 2x = 3y.............(i)

similarly,

3x - 2y = 0
=> 3x = 2y..............(ii)


On taking (i), 2x = 3y

=> x = 3y/2

So ratio x:y = x/y

=> (3y/2)/y

=> 3/2 = 3:2


On taking second, ratio becomes 2:3


If x >y then first is correct
if y> x then second


Hope it helps dear friend ☺️