Find the value of $(x^{2}+y^{2})$ If $x^{3}-3xy^{2}=10$, $y^{3}-3x^{2}y=30$
Find $$(x^{2}+y^{2})$$
I tried but I got nothing, any help please?

$$(x+iy)^3 = (x^3-3xy^2) + i(3x^2y-y^3) $$
gives $(x+iy)^3 = 10-30 i $. If we multiply by the conjugate (i.e. take norms):
$$ (x^2+y^2)^3 = 10^2+30^2 = 1000 $$
we immediately get $x^2+y^2=\color{red}{10}$.
