What is the value of x^3*y^2+2098/xy^2+1/x− x^y, given x, and y are positive integer?

Stat1: x^3+ y^3+ 512/(x^3*y^3)= 24

We know that, (a^+ b^3+ c^3) - 3abc = (a+b+c)*(a^2+b^2+c^2-ab-bc-ca)
where, a= x, b = y, c = 8/xy
So, given, (a^+ b^3+ c^3) = 3abc, which is possible, if (a+b+c)*(a^2+b^2+c^2-ab-bc-ca) = 0, or, (x+y+8/xy)* {x^2 + y^2+ 64/(x^2*y^2) - xy - 8/x - 8/y} =0,
as x and y are +ve integers, so, {x^2 +y^2+ 64/(x^2*y^2) -xy -8/x -8/y} =0 or,
x^2 + y^2+ 64/(x^2*y^2) = xy + 8/x + 8/y, which is only possible, x=y=2. Sufficient to get value of the req. expression.

Stat2: x=y; It is not sufficient.

So, I think A.