Solving a radical system of equations

[echandler]

Nice.

To simplify let u = cbrt(x), v = cbrt(y)
Therefore x = u^3, y = v^3

Thus the original equations become
u^3 - v^3 = 7 #1
u^2 + uv + v^2 = 7 #2


Dividing #1 by #2 gives u - v = 1 #3
cubing both sides gives
u^3 - v^3 - 3uv(u-v) = 1
substituting #1 and #3
7 - 3uv(1) = 1
3uv = 6
uv = 2
and the rest follows as before.

[prabhudasmandal]

The problem is interesting, solution as well. Thanks.

[Halleluyah]

Вот, чтобы не надо было тягать эти кубические радикалы, сделал бы лучше замену