After simplifying the expression, i'm getting

 

An= 3(n-2)/4n

 

and the limit gives me x/y=3/4

 

and in the given question, i could modify it in terms of y as the quadratic expression of y^1/2 ., so if u take y^1/2=M

then u get an expression as

 

M²(3pqr-3r⁴) + (p³+q³)M -4r⁴=0

 

but i am unable to continue from here