Question 9
Let $n$ be the number of real ordered pairs $(x,y)$ solving
$$x^3-y^3=7(x-y),\qquad x^3+y^3=5(x+y).$$
Find the sum of the corresponding $n$ values of $x^2+y^2$, counting repeated values for different pairs.
$$x^3-y^3=7(x-y),\qquad x^3+y^3=5(x+y).$$
Find the sum of the corresponding $n$ values of $x^2+y^2$, counting repeated values for different pairs.