( x^2 + y^2) / (xy) = 8 (1)
(x^6 + y^6) / ( x^3y^3) = ( x^2 +y^2) ( x^4 - x^2y^2 + y^4) / (x^3y^3) (2)
Rearrange (1) as (x^2 + y^2) = 8(xy) sub into (2)
8 ( xy) ( x^4 - x^2y^2 + y^4) / ( x^3y^3) = 8 ( x^4 - x^2y^2 + y^4) / (x^2y^2) (3)
And
(x^2 + y^2) = 8xy square both sides
x^4 + 2x^2y^2 + y^4 = 64x^2y^2
2x^2y^2 = 64x^2y^2 - x^4 - y^4 add -3x^2y^2 to both sides
-x^2y^2 = 61x^2y^2 - x^4 - y^4 sub this into (3) and we have that
8 ( x^4 + (61x^2y^2 - x^4 - y^4) + y^4) / ( x^2y^2)
8 ( 61x^2 y^2) / (x^2y^2) =
8 * 61 =
488