Question 252125
x^2 + y^2 = 6xy

adding 2xy both sides

x^2 + y^2 +2xy = 8xy
=>(x+y)^2 = 8xy ------------- 1

subtracting 2xy on both sides

x^2 + y^2 -2xy = 4xy
=> (x-y)^2 = 4xy -------------2

dividing 1 by 2

{{{((x+y)/(x-y))^2 = 2}}}

so (x+y)/(x-y) = {{{+sqrt(2)}}} and {{{-sqrt(2)}}}