Answer:
x:y = 1:1 or 2:3
Step-by-step explanation:
By a difference of squares, we get:
(y+x)(y-x)=5(y-x)^2
move all to one side:
(y+x)(y-x) - 5(y-x)^2 = 0
take a common factor of (y - x) out and expand and simply the other factor:
(y - x)[y+x-5(y-x)] = 0
(y - x)(-4y + 6x) = 0
By the null factor rule:
x = y
=> x:y = 1:1
or
6x = 4y
=>
x:y = 4:6
x:y = 2:3
