If #3x^2 + 2y^2 = 5xy#, find #x:y# ?

If #3x^2 + 2y^2 = 5xy#, find #x:y#

1 Answer
Shwetank Mauria
Dec 1, 2017

#x:y=2:3# or #x:y=1:1#

Explanation:

Let #x:y=a# i.e. #x/y=a# and #y/x=1/a#

As #3x^2+2y^2=5xy# dividing both sides by #xy#

we get #3x/y+2y/x=5#

i.e. #3a+2/a=5#

or #3a^2-5a+2=0#

or #(3a-2)(a-1)=0#

Hence #a=2/3# or #a=1#

i.e. #x:y=2:3# or #x:y=1:1#

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