let a = (x+y)^(1/2), b= (x-y)^(1/4),
(a, b> =0)
x^3 +(x^2)y -x(y^2) -y^3
= (x+y)·(x^2-y^2)
= (x+y)^2·(x-y)
hence a+b=8, ab=12,
a, b are roots of u^2-8u+12 = 0
u = 2 or 6
(a, b) = (6, 2) or (2, 6)
(x+y, x-y) = (6^2, 2^4) or (2^2, 6^4)
(x+y, x-y) = (36, 16) or (4, 1296)
(x, y) = (26, 10) or (650, -646)
Two solutions
let a = (x+y)^(1/2), b= (x-y)^(1/4),
(a, b> =0)
x^3 +(x^2)y -x(y^2) -y^3
= (x+y)·(x^2-y^2)
= (x+y)^2·(x-y)
hence a+b=8, ab=12,
a, b are roots of u^2-8u+12 = 0
u = 2 or 6
(a, b) = (6, 2) or (2, 6)
(x+y, x-y) = (6^2, 2^4) or (2^2, 6^4)
(x+y, x-y) = (36, 16) or (4, 1296)
(x, y) = (26, 10) or (650, -646)