If (6x^2-xy):(2xy-y^2)=6:1, find x:y

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29 Jun 2013 ratio

If (6x^2-xy):(2xy-y^2)=6:1, find x:y

OPtion

1) 1:2
2) 1:3
3) 1:4
4) 3:2
5) 2:3
6) 3:4
7) 4:3
8) option 4 and 5
9) option 6 and 7
10) None of these

Solution

Divide the Nr and Dn by y^2,
then let x/y=p
we get 6p^2-p=12p-6
6p^2-13p+6=0
solve
p=3/2 and p=2/3
option 8

Correct Option: 8 Best Solution (16)

Vinay Sipani    11 years AGO

let (x/y) = t

=> (6*t^2*y^2 - ty^2)/(2ty^2 - y^2) = 6
=> (6t^2 - t) = 12t - 6
=> 6t^2 - 13t + 6 = 0
=> t = 3/2 and 2/3

Like? Yes (7) | No (1)  

vikrant   11 years AGO

cross multiply (keep it simple)
u get
6x^2-xy=12xy-6y^2
solve it
6x^2-13xy+6y^2=0
so from above multiplication has to be 36 and addition -13
values are -9 & -4
6x^2-9xy-4xy+6y^2=0
take out common
3x(2x-3y)-2y(2x-3y)=0
(2x-3y)=0 or (3x-2y)=0
so x:y either 2/3 or 3/2

Like? Yes (5) | No (1)  

Jigyasa Kumar   11 years AGO

On putting the values it satisfies the equation.

Like? Yes (3) | No   

kaushal kumar verma   11 years AGO

6x^2+6y62-13xy=0, 6x^2-4xy-9xy+6x^2=0
2x=3y or 3x=2y

Like? Yes (2) | No   

shailesh kumar mishra   11 years AGO

6x^2 - xy = 12xy - 6y^2 , 6x^2 - 13xy + 6y^2 = 0 , (3x - 2y)(2x - 3y) = 0 , 3x = 2y or 2x = 3y , x/y = 2/3 or x/y = 3/2 , x:y = 2:3 or x:y = 3:2

Like? Yes (1) | No   

Deepak Sharma   11 years AGO

(6x^2-xy):(2xy-y^2)=6:1
6x^2-xy=6(2xy-y^2)
6x^2-13xy+6y^2=0
(2x-3y)(3x-2y)=0if we take 2x-3y=0then x:y=3:2
& if we take 3x-2y=0 then x:y=2:3
so option 8 is correct

Like? Yes (2) | No (1)  

Devendra Marghade   11 years AGO

(6x^2-xy)/(2xy-y^2)=6/1
x^2[6-(y/x)]/y^2[2(x/y)-1]=6
Substitute x/y=a, a^2[6-(1/a)]=6[2a-1]
6a^2-13a+6=0
6a^2-9a-4a+6=0 or 3a(2a-3)-2(2a-3)=0
a=x/y=3/2,2/3

Like? Yes (1) | No   

Aruna Solanki   11 years AGO

by solving this equation we get x/y equal to 2/3 or 3/2....

Like? Yes (1) | No   

Arushi Baboota   11 years AGO

answer: 4 and 5
6 x^2-x y=12 x y-6 y^2
6 x^2-13 x y+6 y^2=0
(3 x - 2 y)(2 x - 3 y)=0
3 x = 2 y or 2 x = 3 y
x/y = 2/3 or x/y = 3/2
x:y = 2:3 or x:y = 3:2

Like? Yes (1) | No   

nishanthi   11 years AGO

6x^2 - xy = 12xy - 6y^2
6x^2 - 13xy + 6y^2 = 0
(3x - 2y)(2x - 3y) = 0
3x = 2y or 2x = 3y
x/y = 2/3 or x/y = 3/2
x:y = 2:3 or x:y = 3:2

Like? Yes (2) | No (1)  

Parry   11 years AGO

(6x^2 - xy): (2xy-y^2) = 6: 1
6x^2 + 6y^2 = 13xy
dividing with xy
6x/y+6y/x=13
let x/y =a
6a+6/a =13
6a^2-13a+6=0
solving q.equation by a=[13+[169-144]^1/2]/12=3/2 and a=[13-[169-144]^1/2]/12
so a=3/2 and-2/3
x/y=3/2 and-2/3
so answer is 3:2 or 2:3

Like? Yes (3) | No (2)  

Vadivelan M   11 years AGO

baixar musicas gratis

Like? Yes (1) | No   

Jasmine Khan   11 years AGO

(6x^2-xy)/(2xy-y^2)=6/1
6x^2-xy=12xy-6y^2
6x^2-13xy+6y^2=0
6x^2-9xy-4xy+6y^2
3x(2x-3y)-2y(2x-3y)=0
(3x-2y)(2x-3y)=0
3x-2y=0 or 2x-3y=0
x/y=2/3 or x/y=3/2

Like? Yes (1) | No   

piyush jain   11 years AGO

(6x^2-xy)/(2xy-y^2)=6/1
or,6x^2-xy=6(2xy-y^2)
or,6x^2-xy=12xy-6y^2
or,6x^2-13xy+6y^2=0
or,6x^2-9xy-4xy+6y^2=0
or,3x(2x-3y)-2y(2x-3y)=0
or,(2x-3y)(3x-2y)=0
either (2x-3y)=0 or (3x-2y)=0
therefore x:y=2:3 or 3:2

Like? Yes (1) | No   

Arpit Jaiswal   11 years AGO

(6x^2-xy):(2xy-y^2)=6:1
on cross multiplication
6x^2+6y^2-13xy=0
divide by y^2
let x/y=r
6r^2+6-6r=0
(3r-2)(2r-3)=0
r=2/3 or r=3/2
Hence x:y=2:3 or 3:2

Like? Yes (1) | No   

suneetha   11 years AGO

by option verification we will got answer
when x=3 and y=2 and also
x=2 and y=3
we get the 6/1
so answer is option 8

Like? Yes (1) | No