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